The difference is largely though that in the regions where the Civil War was actually fought it was extremely dence. Couldn't go 50 miles without a major city popping up. In the US most cities are extremely spread out only being around coastal regions or otherwise being the designated "economic center" of a state or is literally just the state capital.

In Iowa for example if you just dropped fifty thousand anarchists in Northern Iowa just south of Mason City the closest truly major settlements would be Des Moines or the Twin Cities in Minnesota but even still that's hours of travel by car. You'd be better locking down your collection of small towns then making that kinda coordinated journey especially if you've got fuel shortages or the numerous National Guard outposts that would be in your way along the path. It's not like you're doing nothing. There's hundreds of acres of farmland, wind turbines for basically free power, and enough structure to maintain a nation.

The biggest problem is quelling the populace and just making sure you can convince them to follow since reactionary rebellions from inside are exactly what would end it all.