Probably the less populated interior. Gubmint won't give a fuck about places so remote, though no place is going to be exactly safe. Worst place would be the major cities, which were already running a purge mechanism on its weaker populations by letting their police go off the leash and straight up murder in the open. Just imagine how that will go down in a martial law situation.
I don't know exactly how bad it is going to get, or if this will turn into a civil war. I actually doubt civil war will happen, because they're no rival center of power against the national security state and no class that can really strike out on their own against the regime collectively. Very likely, there will be a sharp declaration of martial law, and a purge mechanism against the current welfare recipients will begin (with the argument that the disabled are being "rehabilitated", i.e. thrown into death camps so the regime can create the necessary social engineering pressure and throw a new group of people into the despised underclass). Once the purge mechanism is activated, it will be very difficult to stop because to fight the regime means risking near-certain death. Eventually a new order will emerge, with either a new constitution or a re-interpretation of existing institutions, and the new eugenic purge mechanism will be normalized. This "revolution" should be largely according to script, and the opposition to such a revolution will prove feeble. More people, I imagine, will seek position in the new order wherever possible, because those are the values the current active generations were raised with. The possibility of any long-term instability is slim to nil, unless the regime starts cracking down too hard on educated workers that are essential to the regime's operation. Very likely the end result of this is some sort of "permanent meritocracy" which will be naturally a hotbed of corruption, and it would set in stone the deal Obama gave the middle class back in '08; torture and death for the lower classes, the immiseration of a large chunk of the native workforce into serf-like conditions, and the promise of vanity for the middle class.