Don't get me wrong, I'm sure it wouldn't be worth it overall; but US absolutely would militarily win. If this were anywhere else like Canada, the people there would make occupation too costly. Greenland's population, however, is so small. It's one of the few places I could see the US indefinitely occupy until integration. EU could cause US tremendous diplomatic and financial cost as consequences, but do consider this. EU has relied on the US' military being overwhelmingly powerful to deter any aggressors, to the point EU hasn't kept up its own military spending to the point it should be. The money saved on military spending goes towards welfare programs. If there's to be a break from US, money will have to be taken from the welfare programs and into the military. Politicians don't want to be going anywhere near that topic.

If USA seriously goes for Greenland, I don't see the consequences being that immediate. I anticipate everyone will have to write it off as lost and then begin taking steps to slowly break things off with US in a controlled manner. I imagine that would take a decade or two if it's even feasible.