The above comment referencing Guns of August has it: the point is not to put up significant resistance, but, like the Minnesotans, force the US invasion force to have to kill or capture them in a way that produces as much negative publicity as possible if they do want to take Greenland.
Indeed the key point is to make sure it is not a bloodless operation. Maybe some pictures of dead white people on the TV will short circuit the part of the republican brain that worships strongmen.
MANPADS are designed to be used against small CAS aircraft. Attacking large transport aircraft effectively requires a considerably larger air defense system. That also assumes you can move a MANPADS within range; the US already controls a large military airfield on Greenland.
The end of the US as we know it happens. Sure the US could win a war ("win"), but the US without US Europe trade, EU turning to China as its main trading partner including in military equipment, no more bases in EU, less access to other parts of the world, and so on. That would be a US that would wither and die.
