The Systemsystem under the Constitution in the USA makes that kind of fracturing pretty hard.
What makes it harder now is that a steady increase in power of the Federal Governmentfederal government has reduced the amount of power that each state has.
If you look at the Civil War in the 1860's, the wedge issue was Slaveryslavery. The precipitation events, though, wasn't Slaveryslavery itself, but the desire of the southern states to leave the Union. The Warwar didn't start until the southern states seceded (left) from the union and formed their own government. There was enough resources in the southSouth that it would do a lot of damage to the northNorth if the secession were alowedallowed to stand. This is kind of a top level view, but it gives a sort of basis for a future conflict.
If you want a Civil Warcivil war, you need a situation where there is a wedge issue, It'sit's big enough for very large groups of people feel it right to leave the rest of the US, and that the resources of the areas leaving are substantial enough to be worth invading those that choose to leave (keep in mind, political capital is a resource).)
To throw out an Idea...idea:
Say there is a wedge issue over Personalpersonal firearms ownership (I'm picking this kind of out of the air).) The 2nd amendment of the constitution gets repealed or some such. Now, Texas, Louisiana, New Mexico, and Arizona decide that they want to keep the right to keep and bear arms and they secede from the Unionunion They decide to form the Republic of Texas.
Here is the kicker that would lead to war: Texas has Oil. Texas has Coastlinecoastline. Louisiana has the Mississippi River Deltariver delta. A bunch of Oil Platformsoil platforms are in the gulfGulf of Mexico and many of the most productive Oiloil refineries. Without those, the Republic of Texas could conceivably cripple the US economy if trade stopped. That would be a logical reason for war.
Of course, if it was just New Mexico that tried to leave, there wouldn't be much of a war because NM would be rapidly overwhelmed and it doesn't have all that much in the way of resources.
So that's what you need. A reason and enough resources to be at stake.