Well, we’d have to wait to see if anything lobbed at us actually exploded, and what kind of bang it made, I think. If, for example, a missile was in the air and seemed to all indications to be heading towards a carrier group’s location, either we would shoot it down, in which case we would with any luck be able to recover parts of it and see what was on it, or we would not/could not shoot it down, and it would do whatever it did, in which case our response would depend on, well, what it did.
Worst case is we don’t shoot it down, it has a nuke, and bad things happen. Even with everything else working right, I suspect there would be a delay of some significance between confirmation of what happened, and any response we’d make. A knee-jerk response would be unlikely to be either as effective or as efficient as something a bit more considered, perhaps.
In the best case, we shoot it down, and find out there was nada or just a conventional warhead. In that case, our response would definitely be more proportional. And if we shoot it down and there actually was a nuke–or the nuke doesn’t go off and we recover it–we’d have an interesting dilemma on our hands I think.
I agree that if, god forbid, by some bizarre confluence of insanity and bad judgment the NK’s actually do make a real nuclear attack on any American forces, the retaliation would be extraordinary. I’m not sure it would be turning NK into a big hole in the ground, though. There are too many strategic reasons to consider less drastic options. But I suppose it’s entirely possible.