A large volcano explosion can toss up enough dirt and dust into the air to block enough sunlight to lower temperatures enough that crops fail; replacing one moderate volcano with a hundred nuclear explosions to cause a similar effect isn't such a stretch.
And did they consider that the best way to kill population centers is with air-bursts, instead of cold-war style ground-bursts? (ground bursts being better at digging out hardened targets like your opponents missile silos) Further, that an air-burst is big on blast effects and radiation, but not so big on ground fires, dust, and fallout in the atmosphere?
Finally, did they look around? Who has 100 warheads? Or even 50 each side to toss at one another? Hmm, only the super-powers. If we start knocking out each other's population centers, it isn't going to stop there. Terrorist states and "limited" nuclear powers are only capable of tossing a hand full of weapons at each other. And that assumes they are willing to commit their entire arsenals, without keeping any strategic reserve... Doubtful at best...
Sounds like more hysteria and fear. Read "State of Fear" - it'll open your eyes.
Of course this would bring up the most obvious question from the rest of the world and our wasteoids, "how can we blame America for it?"