War is unlikely, n korea has been bluffing for years, and there have been similar crises i.e. assassination attempts without outbreaks of war.
Nuclear war; the US presence ensures using nukes would be suicide, because the US would just destroy it... so unless they have nothing to lose no nukes. and apparently they only have around 3/4 nukes with no way to hit Europe or the US so it really hasn't got much to do with us directly
Conventional warfare; Again, US troops are actually in s korea, so if war breaks out on a large scale they would be screwed. China has business with both US and SK, so war wouldn't be... logical...
A few months from now, we'll have completely forgotten about this. probably.