Greenland rejects Trump pledge to make the island American

I believe that Germany and France issued a statement a while ago "warning" the US that borders must not be moved by force. Take from that what you will, but its hard to say.

The reality is that whilst the US would struggle immensely to launch a ground invasion into mainland Europe, the US navy is too dominant at sea for Europe to have much of a chance defending Greenland.

If they really did attempt to take it by force it would be the end of transatlantic-ism and Europe would find it self in increasing danger from its west and eastern neighbors. The only real deterrent to further encroachment at that point would be a European Army capable of seeing of threats from both Russia and the US, and likely Europe would seek new global partners.

(Mandatory: this is just my speculative opinion as an International Relations Student, not an expert.)

The vast ice sheet that covers Greenland would be the new home away from home to various Scandinavian special forces units who would habitually commit assassinations and sabotage against any occupying force. The result would be a massively asymmetric situation similar to Vietnam but in extremely cold temperatures.

I read in some paper a while ago that the American parliament can stop an attack, but if an attack on Greenland can be done quickly enough (within 48 hours was the timespan I read mentioned) Trump could face them with a fait accompi.

This is assuming the US would be capable of having it be a complete surprise attack. In reality (in my opinion) this may not be possible, in which case the Europeans would have time to respond, and the American parliament as well. I have no idea whether they’d be able to stop an attack in advance (though Republican support would obviously be needed for that as well).