Depends. NK would likely launch concurrent strikes against several US cities, and South Korea. The US would memorialize strikes against our homeland just as we do 9/11 or Pearl Harbor. The strikes on South Korea would probably be conventional, to avoid incurring the wrath of Russia and China from fallout, and the associated fallout over North Korea itself.

Then again, that presumes Kim will strike, which he wont. The regime is as stable a dictatorship as we've seen in the modern world surviving 2 leadership changes. They know that staying in power requires looking and acting tough, but only taking action when forced to defend themselves. Short of a strike against NK that prompts defensive retaliation, we won't see anything more than spouting off.