I'm Danish, we don't really care about whether or not Greenland is a part of our Kingdom (I'm sure some people do but it's certainly not the majority in my opinion). That being said it's not like it's ours to sell or give away, so it would be more relevant to ask someone from Greenland. I think the most likely outcome is that Greenland decides to leave our Kingdom and become something like the Marshall Isles.

The whole national security part is a lie though. The US can already do whatever they want up there. Well except for having nuclear weapons, but they'd probably be allowed if they asked.

I think some of our politicians care that they'd lose any form of geopolitical relevance without Greenland, but it's not like our population in general supports that.