Once you have nukes, you think, you'll have a shred of leverage over the US since you'll have the capability to nuke Seoul. With that leverage, you can ensure that your glorious people's republic will continue to prosper without another devastating war. Who cares if you throw the economy under the bus until you're nuclear-armed - that's just the price you have to pay for security.
I personally don't think that the DPRK has any real intention of starting a war - they know that there's about five minutes between hostilities being declared and Pyongyang turning into a radioactive parking lot.
Tom Nichols delves deeper into the topic in both article [0] and book [1] forms.
[0] http://nationalinterest.org/feature/if-america-could-rebuild...
On second thought, if the DPRK were to nuke New York or something, I can't see how the US could afford not to nuke back without looking weak. At the same time, that would probably trigger a nuclear apocalypse scenario pretty quickly with retaliation from China and the like.
But I am not holding my breath either.
It'll only get worse once they've got actual nuclear capability, but it's not like you can just declare that you've decided to sacrifice SK's capital and largest city because bad stuff might happen in the future.
Basically, both China and the US are probably rather worried about the situation there, because the NK leadership is so wacky and volatile; neither side actually wants to take over NK because that'd mean having to deal with their internal problems and a giant, starving population that's been fed crazy propaganda from birth about the divinity of their leaders. No one wants to deal with that problem.