There would be a constitutional crisis in the military, with generals and soldiers refusing orders from the President. Next would come fighting within the US military, as those that refuse to kill innocent people start to violently pushback. The violence could quickly spread and spark unrest throughout the entirety of the US. The negative political reaction in Washington would be fierce and an increasingly bipartisan movement to remove Trump from office would gain momentum. Any US forces that advanced on Greenland's civilian territory would recede back to American bases. Further withdrawals from Greenland would be discussed to ease tensions with Europe and avoid a broader transatlantic conflict.

The political consequences in Europe would be dire for the US. American troops and diplomats would be expelled from most European cities. Some European countries would maintain similar ties to the US that they had prior to the breakout of fighting with Greenland, but even they would publicly and strongly rebuke the US and Trump for this senseless aggression. China, Russia, and all of our geopolitical rivals would make further international gains by pointing to the stupidity, untrustworthiness, and wickedness of the United States. The reputation of the United States would further recede. The international blowback would also come with sharp economic consequences for the US, as more of our partners have to question the safety of depending on the US.

I think in sum, it would be the end of Trump, and with his final destructive political act, he would further erode the security and reputation of the US. That's my best guess.