I'm sure that some won't behave rationally. But what historical example is there to expect widespread civic chaos?
I can think of a few examples: The LA riots, Watts riots. But to put it diplomatically, some people are different. And even those people knew enough to keep the riots in their own neighborhood.
Mob psychology is difficult to predict. I would guess that fear may have a calming effect.
The only two data points we have for nuclear weapons employment were against a culture with a near-fatalistic sense of duty and a tradition of subordinating one's will to that of the group.
Against Americans...I would argue that our greater emphasis on individualism will tend to create a much more chaotic reaction.
If anyone in the target area knows anything about nukes, but doesn't know anything about how to shield against fallout, he will attempt to get the hell out of there immediately.
Meanwhile, a bunch of folks, ignorant of nuclear weapons effects, will try to get their injured fellows (or themselves) to medical attention. Remember, communications are going to be OUT. Passing information to the populace is also going to be difficult, because many of them will have ruptured eardrums.
You basically are betting the mortgage money on a perfectly rational response, in the absence of perfect knowledge of what the rational response is.