Just a quick thought on this and on the broader question. There are some pretty clear reasons for wanting to do something about the current regime in North Korea. But when people discuss what should happen, the common refrain seems to be treating China like a teenager that wants oh so badly to drive mom and dad's car, but just hasn't proven himself yet. I'm fairly certain this article explicitly mentions the notion that the US has tried to get China to feel like it has some "responsibility" for taking care of this issue, and I think this is part of the problem.
Sure, China has some responsibility for North Korea, but it also has a lot to worry about in the event that North Korea implodes–Nuclear weapons, a potential refugee/humanitarian crisis, etc. China is probably acutely aware of the costs related to any of the potential "fixes" for the North Korea problem. That said, I think the debate in the US sends the signal that China would be bearing those costs alone. Sure we can tie some rewards to Chinese action on the issue, but is reducing the number of US troops in South Korea really that enticing at this point? Does anyone in Beijing really think the US would use the collapse of North Korea as an opportunity to invade China at this point in the game? The US and China are intimately linked through trade and US government borrowing, and it really seems like US troops maintain a presence in South Korea more for the benefit of the North Koreans than anyone else. For all our talk of multilateralism it really seems like the policymakers pushing China to take action have offered very little in the way of measures that would help to spread the costs of dismantling and rebuilding North Korea around to other countries aside from China. I think it's probably implicitly assumed that the South would take up some of the slack, but this seems to be rarely highlighted. And with a relatively substantial military presence, and a more general stake in regional security, I'd think US policymakers would be coming up with something more substantive and palatable than merely trying to tell China to take some responsibility. But considering that we're involved in two wars and still coming out of a severe economic crisis, I'd say our ability to help is comparatively limited.
Ultimately, what is China's incentive to take any sort of hard action against North Korea if they know that they are also going to suffer all of the risks/costs associated with doing so? If there is a fear of serious future competition between the US and China in the region, continuously urging China to take unilateral responsibility for regime change in North Korea can only fan the flames of skepticism regarding US intentions.