Of course US will get involved with the situation. We basically own South Korea. A little history lesson for those who may not know. There was a war with Korea that eventually went cold and the land that US took became South Korea. We even have troops stationed in the area, it's a highly influenced by US.
Anyway back to the point, if Korea starts a war they would lose and there's no question about that. There only ally is China, which happens to be people we're on good terms with because of our business. China being the number one producer and US being the number one consumer, with that at hand the chances of China going against US are slim to none.
As I'm sure you've already heard, Korean warheads can't reach US, but they can definitely reach South Korea. The problem with that is the moment they launch one they are surrounded on all sides by countries who are allied with the US in some way, because of that North Korea will not go along with war, it's just a losing battle.