First, this is a highly speculative answer, but it pretty much has to be, given the subject involves predicting the future. So consider this my best guess, but not at all authoritative.
You will start to run out of gasoline in just a few years. Once that's gone, you might be able to keep motorized things running for a few more years on biofuels and such, but then you will also start to run out of consumables like motor oil, because they also break down after a few years. Within at most a decade or two you will no longer have fossil fuel powered vehicles and tools. That's devastating. And once the people move out to the country to get away from the disease and danger of the city, the lack of motorization will make it very hard and expensive to bring scavenged goods from the city to the people.
Wind and solar power will start to fail after 20 years or so, and eventually the composites in fan blades and bearings in motors will fail, and solar cells will degrade. You might be able to find enough spares to keep some solar power going for few decades or maybe even 100-200 years, but not at industrial scales. You won't be driving solar cars or running solar powered factories.
Coal will make a big comeback. It's an easy fuel to use with low tech, it can power steam boilers and home heaters, and there's a very nearly unlimited supply available. You could be a coal scavenger for a long time.
So the biggest problem your society will face in the medium term will be energy. Energy is the lifeblood of a modern society, and enables our standard of living. If you go back to water wheels or manual labor, your standard of living will crash back to pre-industrial levels.
Most foods will be spoiled within a few years to a decade. Now you will have to grow your own. Without mechanized farm machinery, you won't be quite back to subsistence farming, because there will still be available fertilizers and knowledge of scientific farming practices, but it will be close. The standard of living of the people will plummet. There won't be enough people to maintain old infrastructure, or enough free time to invent better ways to do things. And if there are a lot of people, they will probably starve. The carrying capacity of North America is greatly dependent on mechanization, high energy farming, and the ability to transport food long distances from fertile regions to the cities. All of that will be lost.
In the longer term, bearings will corrode, electronics will fail, medicines will all be extinct, concentrated fertilizer will be used up or unusable, and you will be utterly unable to replace it. Within a couple of generations you will be back to a small subsistence farming population, too busy growing food and staying alive to maintain old infrastructure. Flora and fauna will take over cities, roads will break down and become impassable, and eventually you'll have a world of small groups of subsistence farmers living out on the land and the cities will be largely abandoned.
Once this state is achieved, a technological society would have to be rebuilt from scratch, and to do that will require hundreds of millions of people. So your future recovery back to today's standard of living will take as long as required to grow the population back to pre-apocalypse levels. Hundreds to thousands of years, depending on the birth and death rate.
None of this includes the very real possibility of conflict. Getting people to peacefully cooperate while their standard of living craters is not easy. One possible scenario is a return to hunting and gathering because farming communities become rich targets for attack.
Things like steel will be available for a long time, but without concentrated energy you won't be able to smelt it very well - at least in quantity. You will be able to re-melt it into swords and hand tools and such using ancient techniques, but you won't be building new metal buildings or anything like that.
Your eventual society will probably look a lot like what the first settlers in America had, although the remnants of society will give you a permanent collection of better hand tools, and you might be able to keep interior LED lighting going with small scavenged solar panels. You might also have better housing, and there will always be enough steel and old wood beams and such to enable it.
As for scavenging being economically feasible... What economy? You will be back to bartering immediately, and money will be worthless. Barter makes it harder, because you have to find the person who has exactly what you need, and you have to hope that he needs what you have. I would suspect that there will be scavengers going far into the future, but the impact of scavenging on the overall standard of living of the people will diminish rapidly over time as old stuff degrades and the people lose the free time needed to scavenge as they work most of their waking hours growing enough food to survive.