Captain Ed discusses an Australian article in this post about how the Chinese government may be considering regime change in North Korea. It doesn't seem to be that China would go through military action to do this, but they have high enough stakes in preventing the sudden collapse of North Korea that it must be at least one of their considered options in stabilizing North Korea.
Not to bring back Cold War containment strategies, but I can't imagine that military action against North Korea isn't being considered by the administration. The current regime in North Korea was, until recently, crazy but mostly toothless. If it becomes a Chinese puppet, the South Koreans might find themselves rather uneasy, and understandably; it was the Chinese who helped the North Koreans in the original war.
Would the US go to war with North Korea? Not without the approval of the Chinese, and I doubt they'd let the US expand its hegemony in the region so easily. Japan already gives them cause for concern; another western foothold in the area might be more than they could bear.
Would the US go to war with China over North Korea? It's a possibility, though I'm hesitant to guess how much of one. With troops invested in Iraq, the military is going to be less interested in starting a full war elsewhere in the world, especially one as taxing as a war with China would be. Could the US win a war against China? Again, with troops in Iraq, it would be a much harder endeavor. We already have a military presence in South Korea, but not nearly enough to fight the full might of China. I hate to say it, but I imagine the only way to quickly and easily win a war against China would be the use of nuclear weapons, and I don't think anyone wants to open that Pandora's Box.
I ask whether or not the US would fight, but I imagine that South Korea would be a bigger instigator in this. I imagine their government having more to say about China taking over North Korea than the US would, but if South Korea went to war with China, we would be dragged into the fight almost immediately.
So, if it comes to it, does North Korea have the strategic significance that the US would fight China for it? Maybe. I can't say either way. I suppose we wait with baited breath to see what happens over the next several months.