I doubt it raises the costs of invasion very much. I don't expect the Danish to fight to the last man. If shooting starts, they will evacuate quickly.
But it meant that the US will have fired shots at NATO soldiers, rather than just walking in and declaring themselves in charge. That raises the political and economic stakes, if not the military ones.
It's making absolutely clear that this means the end of NATO, and puts all EU/US relationships in doubt. It could even mean that we were automatically at war. They're hoping that somebody around the President will consider that too high a price to pay. Which is a long shot, but is probably the least-worst option.
But it meant that the US will have fired shots at NATO soldiers, rather than just walking in and declaring themselves in charge. That raises the political and economic stakes, if not the military ones.
It's making absolutely clear that this means the end of NATO, and puts all EU/US relationships in doubt. It could even mean that we were automatically at war. They're hoping that somebody around the President will consider that too high a price to pay. Which is a long shot, but is probably the least-worst option.