Well, let's actually TRY to follow the idea of the OP (suspension of disbelief people, you have to actually imagine that scenario and act on it, rather than just saying "Baah...that'll never happen..."). This very much sounds like a Tom Clancy premise.
I'd say we'd pretty much be at an impasse/standoff. First of all, it really depends on what terrorists do it, since there are several different varieties. You could have splinter cell extremist groups for a variety of causes here in the US, mercenaries/militants from other countries, etc...
The whole "we don't negotiate with terrorists" attitude only gets more people killed, so there would hopefully be an attempt to negotiate, especially if there is a live nuke present. We'd attempt to meet their demands while assembling a counter-terrorism team (wait...you mean things like in Counterstrike DO Exist? zOMG!), and if the CT team fails (usually unlikely, but can happen depending on how good/prepared the terrorists are) then we have to follow the US chain of command...if we lose the President, VP comes into power, and then the Senate Pro Tem, etc etc.
If the CT team succeeds, then a full on investigation will be carried out to determine the terrorist sources, and (if we have a proper government in place) we'll hunt down and attempt to eradicate that ONE PARTICULAR CELL of terrorism, or attempt to negotiate with them to stop their wishes of wanting to commit atrocities. Killing terrorists does not stop terrorism; on the contrary it's very much a Hyrda effect.