Again, I haven't seen the show, so I'm handicapped by not knowing the details of the premise. I looked up a few things, and apparently the premise is 23 major cities hit by atomic attack.

Frankly, there is no plausible scenario for this happening, not in the show's premise, or in someone's worst paranoid real-world nightmares.

I expect that a more plausible scenario, an attack on one or maybe two cities by some smuggled devices or a rogue missile attack, would certainly result in increased controls by authorities, particularly in the former case (terrorism). I don't see it getting too much past the point that was routine for many Western nations during WWII (rationing, curfews, military patrols, increased security, reduced freedom of activity). When the war was over, things went back to normal.

Most films I've seen dealing with this subject, like "The Day After," or "Testament," showed a lot of unfamiliarity with the subject.