More than one country = 2. Russia (8400) and China (390).
Well, four, I suppose, so long as you want to fear Britain (2-300) and France (a surprising 350).
India has 60-90 and Pakistan 24-48. I submit that, delivery systems issues aside, those numbers are inadequate to achieve your goal of taking out a dozen major cities (one nuke |= one city).
These figures from
http://en.wikipedia.org/wiki/List_of_countries_with_nuclear_weapons. If you don't like wikipedia, feel free to supply me with better numbers.
Then there's the fact that, according to
http://nuclearweaponarchive.org/China/ChinaArsenal.html, China has only 20 ICBMs in its arsenal.
As to your scenario, let's assume that "they" take out those dozen major cities. Best I can figure, that's about 60 million people. A lot. It leaves about 210 million really, really pissed people. Are you suggesting that they'd just roll over and invite the bad guys in? Isn't this America, home of the brave, and all.
But more to the point, what has this hypothetical attacker accomplished? I mean, is this just somebody who hates us for our freedom, or did they have something more in mind than the obliteration of the US?
Generally speaking, wars are about resources or territory (or a combination of the two). There may have been some fought for pure braggin' rights, or just purely out of spite, but I can't call those to mind.
So, again: who's going to do this? If either Russia or China is looking for space/arable land, there are places much closer and easier to control. If the bad guys you posit are looking for resources, there are much better, easier targets. What--they're coming for our oil? For our amber waves of grain? Again, there are closer, softer targets. Maybe even ones where you don't have to wait for the fallout to clear before you can farm them.
There's only one country since WWII that has flitted about the world indulging in military interventions, and it's not going to invade the US because it's there already. I ask you again: who is this threat to US sovereignty, and what is their purpose for invading?