Their piss-poor attempts at building ICBMs would never reach Alaska, Hawaii, hell even Guam, no matter what the statistics say. But launching 1 with the intent of hitting US soil would be a tipping point for the Obama administration. I'm not convinced they'd immediately go nuclear, due to the civilian casualties. Not that they've exactly balked at the civilian casualty rate from UAV strikes in Afghanistan/Pakistan.
All this is moot anyway, as batshit crazy as Kim Jong-Un is, even he can't be that stupid? The guy's pretty well educated, surely no amount of indoctrination could override that?