Regarding an 'invasion' of Greenland, it would actually be done in a day, and I highly doubt an effective insurgency would form. The US already has military control over the territory, and the population is way too low and concentrated to offer opposition.
This is implicit in the reaction of the EU: If the US takes over Greenland, Europe will close down all American bases in Europe.
This is what makes this particular foreign policy so incredibly stupid: The US already gets everything it needs from Denmark/Greenland. The US is considering throwing away European allies to have their flag be bigger on a world map.