Ruralites can (and often already do) drive 4WD vehicles and run generators (or nowadays solar + batteries) for power. In an extreme case, they'd be at least somewhat willing to revert to horses and candles (hell, quite a few might even consider that fun). It'll take adjustment, but it ain't an insurmountable problem.

The far bigger concern is that very few (if any) rural towns in the US have self-sustaining food supplies. Cut off their access to the outside world, and there's a very high probability that they'll starve just as quickly as a larger city will. American agriculture has shifted hard from diversified/robust subsistence farming to large-scale industrialized monocrop farming, so you'd have to rewind a century or so of "progress" in order for a rural town to be able to feed itself. This is also not an insurmountable problem, but the effects are quite a bit more dire.