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Pretzel The same thing happened during the War of 1812. The USA very stupidly declared war on what's now Canada and the silly asses tried to annex Canada 7 times and lost 7 times, thereby retreating south of the border once and for all.
This was no different than the US retreating from Panama when it lost it's invasion of 1989, nor when the US retreated from Vietnam when it lost due to gross incompetency at jungle warfare, nor when the US retreated from Iraq when it lost after discovering their US Intelligence was fake, nor when the US retreated from Afghanistan after it lost due to gross incompetency at mountain warfare.
The USA has lost every war it ever started in the last 214 years and only maintains a 61% average over that same time period in coming out the winner of any pre-existing war the US ever stuck it's greedy nose into.
Americans by their very nature are not warriors and never have been as evidenced by the US military's track record. There isn't a doubt in my mind that the US would back down from Greenland, no different than it backed down from the Brits during the War of 1812 when the US tried 7 times to annex north of the Canada/US border.