Boundaries are historical contingencies. A key point is that you want not an alternative history, in which we look at possible historical forks in the road that we could have taken, and instead want a future North America that could evolve from the starting point that it has today. How and why that happens would dictate the result.
Fortunately, we have a number of recent examples of countries breaking up to imagine how that might happen.
Breaks Along Existing Boundaries
In general, there is an imperfect tendency in a breakup to follow the boundary lines of sub-national regions.
In the U.S. Civil War, Virginia (which broke into Virginia and West Virginia) was the only political unit not to end up on one side or the other, although there were arguably a few counties in a few border states that resisted their state's decision to stay in the Union. Even the split of Virginia and West Virginia tracked county lines and political/ethnic divisions.
In the breakup of Yugoslavia, the first step was a break up into constituent states within the country (Slovenia, Croatia, Bosnia, Serbia and Macedonia). Then, there was a second order split off of one of the two autonomous regions within Serbia (Kosovo) that was ethnically distinct.
The division of Czechoslovakia into the Czech Republic (a.k.a. Czechia) and Slovakia, tracked pre-existing political division that in turn matched ethnic lines fairly closely.
In the breakup of the Soviet Union, for the most part, top level Soviet Republics each broke off without incident, while sub-Republic autonomous or culturally distinct areas within Soviet Republics retained their boundaries.
The Russian autonomous areas in the Caucasus mountains weren't thrilled with this leading to several military actions there, most notably the Chechen insurgency that was ultimately resolved when a strong Chechen leader seeing that the gig was almost up declared loyalty in a more or less personal way to Vladimir Putin on behalf of people loyal to him.
The other issue was the Ukraine where the country was strongly geographically divided between pro-Russian regions in the east and pro-Western regions in the West. Russian unilaterally retook the pro-Russian leaning political unit of Crimea with its pre-existing boundaries. Notably, Crimea was a late addition to the historical territory of the Ukrainian Republic. Russian efforts to acquire provinces elsewhere in Eastern Ukraine have been inconclusive despite military aid to insurgents and Russian military forces deployed there.
The 19th century United States of Central America quickly fractured relatively cleanly along the boundaries of the member states.
Many countries with a colonial relationship are split off with existing boundaries relatively cleanly, e.g., India, Canada, Australia, New Zealand, Finland (from Sweden), Iceland (from Norway), although problems can follow when the countries that result are not nation-states and have different ethnic majorities in different regions (e.g. Canada's tensions between Quebec and English Canada and India's tensions between Hindus and Muslims; but not Finland which has three cultures (Swedish, Finnish and Saami) but with the dominant Swedish and Finnish populations geographically overlapping).
The division of India was notable for being conducted by an outside "expert" based upon demographic data. It was very bloody but at least was short lived compared to the long running insurgencies associated with most ethnic divisions. But, disputes over the border in Kashmir remain to the present day and were the source of violent insurgency for a prolonged period.
Breaks Along Ethnic Lines
Splits along ethnic lines rather than from the collapse of a central government that frees all member top level subdivisions are almost always preceded by long, violent military insurgencies.
The Eritrea-Ethiopia split, the South Sudan-Sudan split, and the India-Pakistan split all traced geographical divides between ethnicities rather than existing subnational boundaries (the subsequent split of Pakistan into Pakistan and Bangladesh involved a country with disjoint territory and ethnically very different populations despite a shared religion in each of the two territories). Each of these followed long, bloody insurgencies and ethnic violence lasting decades.
The split of Ireland into Northern Ireland (which remained loyal to English colonial rulers) and the rest of Ireland (which rebelled and secured independence) was also drawn primarily based upon ethnic geographic division rather than pre-existing political boundaries and resulted in decades of continued ethnic violence in Northern Ireland (spilling over into England).
Notably, despite the fact that Northern Ireland's Protestant majority is largely a result of migration from the Scottish borderlands (which also was the primary source for the population of Appalachia in the U.S.), no one has ever seriously proposed merging Northern Ireland and Scotland into one political unit to which its ethnically Irish Catholic minority feels no ties.
Yemen was divided on ethnic lines after an insurgency and all hell has broken loose resulting in blood civil war/proxy war when an effort was made to merge it back into one state in fairly short order.
Columbia was de facto divided between a FARC narco-state in the interior and a rump state elsewhere resulting in a long civil war that voters rejected a treaty resolving in a recent election.
Many countries with geographic ethnic divides have long running civil wars that don't in the end cause the split of the country. Nigeria had an east-west civil war and is now waging a north-south one. Sri Lanka has a long running ethnically based Tamil civil war.
Many regions of the world - sub-Saharan Africa, the Middle East, large swaths of Europe, Brazil v. Spanish South America, Yugoslavia, N. v. S. Korea, W. v. E. Germany, have boundaries (or had boundaries) that were drawn up following the conclusion of major conflicts in great political conferences by outsiders in a moment of an indigenous political vacuum, often with little sensitivity to the concerns or desires of the locals.
Strong Expansionist Leaders
Powerful states with strong leaders swallow up small states - e.g. the United States gobbled up most of North America, Russia expanded to the Pacific, strong leaders unified Italy and Germany respectively, Nazi Germany grew tremendously in its expansion phase. Something like that might unite pieces of the former United States that were formerly fractured.
A scenario that makes sense
I'm going to consider just one scenario that could cause the breakup of many.
Critically, the end result is only metastable, rather than being as stable as the existing boundaries of the North America or Europe. These boundaries and alliances would be young and might be reshuffled and dynamic as political winds and global realities shift over time.
The federal government collapses and states go their own way.
Suppose that three factions emerge in the federal government, none of which is willing to work with either of the others on anything, so there is no longer majority support for any bill in Congress in either house, and no President who must be associated with one of the three factions can command majority support for anything. It doesn't really matter much which particular factions they are, although post-collapse alliances might track faction lines.
Think hard about some scenario that could create three non-majority roughly equal factions that mutually hate and distrust each other and has some regional skew to it.
Imagine in this scenario that Congress fails to produce a budget year after year, with no faction able to command a majority, and no President able to get many cabinet officers or judges appointed. Federal workers and federal government contractors start quitting when they stop getting paid.
No one takes meaningful action to enforce federal laws.
After a while, some states stop bothering to even try to hold elections for federal offices, and people cease to bother trying to file cases in federal courts.
Maybe a rare consensus in the dysfunctional Congress approves the secession or reorganization of states in separately negotiated interstate compacts. Eventually they go ahead with interstate compacts without honoring the constitutional requirement of Congressional approval.
State lines would remain in tact except by mutual agreement. I could see Washington State and Oregon transfer their territory to the east of the Cascades to Idaho.
Economies of scale and a lack of benefit to having their own U.S. Senators in the absence of a federal government might encourage a merger of North and South Dakota, of Montana and Wyoming, of North Carolina and South Carolina, of Kentucky and West Virginia (and maybe Indiana too - which has an almost Appalachian conservative culture despite its location and topography outside Indianapolis and the northern coast), of Michigan and Wisconsin, of Oklahoma and Texas.
A grouping with Montana-Wyoming-Colorado and New Mexico could work.
The six New England would be a natural candidate to merge into some sort of federal country, or perhaps to realign themselves as new Canadian provinces, a la Alaska.
The Mid-Atlantic States (Pennsylvania, New York, New Jersey, Maryland, Delaware) and the District of Columbia would probably form a unit and might even manage to get Virginia to break up with Northern Virginia joining it instead of a Southern Confederacy.
The Mid-Atlantic states might be part of the same political entity as New England (if DC got statehood and Northern Virginia joined it would have thirteen states just like the original thirteen U.S. colonies, with many of them having been original colonies). or might just have close ties with New England.
A federal type country made up of former Confederate states, minus Florida and Louisiana (which would go their own ways), but possibly plus some of the Appalachian border states (perhaps a merged West Virginia-Kentucky-Indiana or perhaps all three of them separately).
Texas might have close trade relations with, but not join, this new Southern confederacy, a bit like the non-EU member Scandinavian countries relationship with the EU.
I could see a loose confederacy tying the Dakotas, Kansas, and Nebraska. Missouri and Iowa would be more likely to join them than a grouping that included Wisconsin, Minnesota, Illinois, Michigan and maybe Ohio too in a Midwestern Confederacy.
Rump Washington State and Oregon, along with California and Nevada might merge.
In the West, Arizona is the odd state out. It would probably be more inclined to either stand alone, or join a greater California, than to affiliate with New Mexico or a greater Utah. New Mexico and Arizona aren't very similar culturally, ethnically or politically, and while there are lots of Mormons in Arizona there aren't enough for it to be comfortable joining a greater Utah with the Mormon faith as a central focus of national identity.
Hawaii would probably return to independent status as would Puerto Rico.
Expanded Idaho and Utah (both heavily Mormon) might merge and might try to secure rural Nevada (which makes up most of the state, has very few people, and is heavily Mormon).
To Recap Where 50 states and D.C. and it territories would end up
Each of the smaller successor states to the U.S.A., each with their greater degree of internal political consensus, would be much easier to govern than the entire United States as it exists today.
But, diplomacy that was never necessary before between these factions would now become a major preoccupation.
Also, some successor groupings would be more tightly bound than others and with the U.S. Civil War's spell discouraging secession broken, internal politics would always be hunted with exit threats (some more credible than others) in the six federal or confederate successors that would be present.
The DSA would probably not have a legislative branch or judicial branch that handled private law cases. It would have a high court of military justice and some administrative law courts and would be run by unequal delegates of the eleven member nations a bit like the European Community before it became the E.U. or NATO or the UN Security Council with its peacekeeping units. Its headquarters would be in Denver because of its central location and because the Rocky Mountain Confederacy would be a weak member of the alliance since strong members would be too envious if the headquarters were located in one of the stronger or more unified members of the DSA.
Organizationally, the DSA military would be more like NATO with significant distinct member state sourced military units, than like a truly unified military force. It would probably also be underfunded relative to the current military and riddled with distrust between member forces who would fear both a bid for reunification a some coalition of member states and a member state gaining advantage that it could use against another member state.
The DSA would probably not be able to maintain a unified front on trade or immigration policy which have always been the source of strong regional divisions in the U.S.A.
The Eleven Member States Of The DSA
The Republic of Hawaii, which would accept American Samoa, Guam, and the Commonwealth of the Northern Mariana Islands, and other U.S. possessions in the Pacific as dependencies with a similar legal status relative to it to what they had with the U.S. The Republic of Hawaii would have strong positive ties with Great California but would have no need to share governance with it. Ironically, it might need a military alliance with Japan as well as the DSA to protect itself militarily from Chinese and North Korean and Russian aggression.
Greater California (Washington State and Oregon west of the Cascade Mountains, California, Reno, Las Vegas and a strip of former federal military bases between them, Arizona). Not clear how this would be organized internally, probably initially along pre-existing state lines in a federation until reformed via referendum to subdivisions that break up California into two or three or four units. Rump Nevada might be realigned as well. The central government would be quite powerful. There would be tension between Greater California and Greater Utah over the split up of Nevada. It would be one of the more wealthy successor states.
Greater Utah (Washington State and Oregon east of the Cascade Mountains, Idaho, Utah, Nevada except for the major cities and strip between them that join Great California). This would probably become a unitary state rather than a confederacy. This would be fairly isolated from the outside world in part out of their own inclinations, with Greater California and Canada providing the easiest access to the sea and would probably have decent ties with the Rocky Mountain Confederacy. Without the need to form coalitions with other Red State politicians, Great Utah's political sensibilities would diverge quite a bit from their current positions over time. It would be a somewhat poor successor state (in part due to large family sizes with only average levels of productivity).
A Rocky Mountain Confederacy with 4 member states (Montana, Wyoming, Colorado and New Mexico). This would need to maintain peace with some combination of Canada, Greater Utah, Greater California, the Great Plains Confederacy, Louisiana and Great Texas to reach the outside world, but wouldn't need all of them. Its best tool to buy this peace would be its control of its neighbor's water supplies. It is not a good candidate to merge with any of it neighbors and would be a particularly fragile confederacy of states that have less in common with each other than some of the other groupings. The central government bureaucracy would be very small and its institutions might be quite weak and consensus oriented. It would be middling in prosperity and have lots of variation in wealth and sources of wealth between member states. Mineral resource exploitation firms would be powerful and there would be a fear of undue Greater Texas corporate influence in its governmental affairs.
Greater Texas (Texas and Oklahoma). This would be a unitary state not a confederacy, but would have strong ties to the Great Plains Confederacy and the Southern-Appalachian Confederacy. It would use the death penalty heavily and swiftly without federal court interference. Its economy would rise and fall with the state of the international oil market. It would grow authoritarian as a heavily petroleum based economy.
A Great Plains Confederacy with 5 states (North Dakota, South Dakota, Kansas, Nebraska, and Iowa). This would probably secure access to the outside world via ties with Canada, Greater Texas and the Midwest Confederacy. North and South Dakota might merge in this scenario turning it into a four state confederacy instead of a five state confederacy. It would export farm products, oil and natural gas. It would welcome seasonal "guest workers" but would otherwise be quite xenophobic. The central government would be stronger than the Rocky Mountain Confederacy or the Midwest Confederacy, but weaker than Greater California, the Federated States of Greater New England, or the SAC. There would be only modest internal division over many key policy issues. It would have a relatively stable economy despite its commodity dependency relative to Greater Texas.
A Midwest Confederacy with 5 states (Minnesota, Wisconsin, Illinois, Michigan and Ohio). It could access the greater world via the Great Lakes and St. Lawrence seaway. Mercantilist economic policies designed to reinvigorate manufacturing would be popular here even if they didn't work well. This would have a weak central government but stronger than the Rocky Mountain Confederacy particularly in the areas of trade and industrial development.
The Free State of Louisiana It could manage independence due to its strategic location and long standing differences in its legal and governmental system from the rest of the U.S. due to its French traditions that give it a unique identity. Rising sea levels would be a great concern. Mississippi River and Gulf of Mexico maritime trade, oil and gas, and tourism would all be important to its economy. It would become a major shipping flag of convenience like Liberia and Panama.
Most of Florida a.k.a. The Sunshine Republic (on its own and minus the panhandle which would instead join the Southern-Appalachian Confederacy). Like the free state of Louisiana, it could stay connected to the outside world with its strategic location. The Sunshine Republic would try to disavow a lot of its Southern cultural baggage, would embrace its Latino and Jewish diversity, and would position itself as a tolerant international tourism and warm weather agriculture destination if it could manage it. It would lose much of its territory in the Everglades to rising sea levels and would invest many billions in seawalls that would allow cities like Miami to persist in the face of rising sea levels. There would be tensions between the Sunshine Republic and the SAC over the split up of Florida, and the Sunshine Republic would be outgunned militarily and hence very dependent upon military and diplomatic allies for its continuing independence.
The Southern-Appalachian Confederacy (i.e. "The SAC") with 13 states (Missouri, Kentucky, Indiana, West Virginia, Arkansas, Tennessee, Mississippi, Alabama, Georgia, the Florida Panhandle, South Carolina, North Carolina, and Southern Virginia). The divisions between Appalachia, Ozark culture and Southern culture aren't currently very salient, so this could work with thirteen states. It would declare itself an Evangelical Protestant Christian nation, even though it wouldn't have a formally established church. (Florida, Louisiana and Texas which have significant Catholic populations, and in Southern Florida's case, a significant Jewish population as well, all of which were states that were part of the Confederate States of America wouldn't be present to muddy the waters). It would adopt the Confederate flag. It would be socially conservative and very militaristic and interventionist. It might even legalize dueling in the course of an effort to reestablish a new national identity. It would use the death penalty heavily. There would be tensions between the SAC and the Sunshine Republic over the split up of Florida (it would bully the Sunshine Republic to some extent) and between the SAC and the Federated States of Greater New England over the split up of Virginia (two of the most powerful successor states with very different military cultures).
The Federated States Of Greater New England with 13 states (Maine, Vermont, New Hampshire, Massachusetts, Connecticut, Rhode Island, New York, Pennsylvania, New Jersey, Delaware, Maryland, District of Columbia, Northern Virginia). It would have something very similar to the current U.S. Constitution. This would become a liberal utopia with a sprinkling of libertarian and Puritan thrown in. It would have tensions with the SAC over the split up of Virginia. It would be one of the more wealthy successor states.
Outside the DSA
Puerto Rico would declare its long overdue independence. It might not join the DSA. It would have historically strong ties to the Federated States of Greater New England where many Puerto Ricans live, and would fear military aggression from the SAC. It might seek stronger diplomatic ties with Mexico and other countries in Latin America and might join a Latin American equivalent to the DSA that might emerge in the face of less predictable neighbors in Anglo North America.
Alaska annexed to Canada. This would probably be a poor fit culturally and leave succession rumblings sounding on and off. Alaskans are cold weather cowboys and not a "civilized" as Canadians. Canada wouldn't be part of the DSA. But, given the great distances involved and the small number of people involved, there might be enough elbow room to prevent conflicts from bubbling over. Alaska might be broken into several parts - a Northern and Bering Strait Alaskan territory, a coastal greater Juneau province, and a greater Anchorage province, perhaps, to more manageably integrate it into Canada since it might be hard to digest whole.
The U.S. Virgin Islands would merge with the British Virgin Islands and would absorb other Caribbean U.S. possessions (except Guantanamo Bay which Cuba would reclaim) making it part of the U.K. It wouldn't be part of the DSA and few people would notice the difference. With the U.K. Navy defending it, it wouldn't have to worry about military and international affairs.
Where there was once Canada and the U.S. (except the U.S. Virgin Islands), there would now be 13 sovereign units of varying sizes.
The hot, long lived military insurgency conflicts would be in the five places where state boundaries weren't followed: eastern Washington State and Oregon, rural Nevada, the panhandle of Florida and Virginia, except to the extent that they were cleanly brokered political deals.