My guess is they both start to look like Hezbollah. That is to say, they will have associated paramilitaries, and may start providing social services as the state itself breaks down.
How does this translate geographically? What areas do you think Republican America and Democratic America will come to control if they're the ones doling out essential services in their turf?
Rural and exurban areas are Republican, cities are Democratic. Suburban areas will be a jagged patchwork of different fiefdoms. Recall the maps of regime vs. rebel controlled Damascus from a few years back.
