South Korea's got this. No need for us to get involved.
That said, I think this is really more of an indication of how bad the change of power is going for the new dictator. North Koreans are raised to believe that the world is jealous of its accomplishments, wealth, and overall awesomeness. It is only through the efforts of their great past leaders (such as Kim Jong Il) that the rest of the world has not come strolling in to take everything away (like what happened in the South... or so the propaganda goes).
The context of all of this has been: "The U.S. continues to act aggressively towards us, blah-blah, we will defend ourselves!"
Why broadcast it to us? Simple - to provoke a response that gives them the opportunity to take video and increased diplomatic efforts and twist them for propaganda purposes to show the people that the rest of the world is a pressing concern and distract from internal politics and feuds.
Which does mean that it is possible for the behavior of North Korea to get even more erratic as time goes on. While a nuclear strike against the U.S. is well beyond their technological capability (in terms of ballistic missiles... their warheads are simply too big to be delivered by anything short of a Saturn V - old-style bombs that are just not all that efficient and very bulky). Though it is possible that they could conspire with other interest groups and nations to organize a clandestine strike utilizing a cargo ship or something of the like.
I just wish they'd shit or get off the pot. If they are going to do this, let's go and get it over with. I'll gladly deploy to Korea - an environment I'm much more comfortable with than the sandbox. That, and there's some old friends I have there that I'd like to stop by and say hi to, after helping to save the day, of course.
