It takes some patience to unwind all of the nonsense here.
The base at Pituffik (formerly Thule) only exists because Denmark permitted the US to build it at a sensitive time. It has served for decades as a central part of the US’s nuclear armoury and then as an early-warning system against Soviet and then Russian nuclear attack.
When Vance says that Denmark is not protecting Greenland and the base, he is wishing away generations of cooperation, as well as the Nato alliance itself. Denmark was a founding member of Nato, and it is already the US’s job to defend Denmark and Greenland, just as it is Denmark’s job (as with other members) to defend them in return.
Americans might chuckle at that idea, but such arrogance is unwarranted. We are the only ones ever to have invoked article 5, the mutual defence obligation of the Nato treaty, after 9/11; and our European allies did respond. Per capita, almost as many Danish soldiers were killed in the Afghan war as were American soldiers. Do we remember them? Thank them?
The threat in the Arctic invoked by Vance is Russia; and of course defending against a Russian attack is the Nato mission. But right now the US is supporting Russia in its war against Ukraine. No one is doing more to contain the Russian threat than Ukraine. Indeed, Ukraine is in effect fulfilling the entire Nato mission, right now, by absorbing a huge Russian attack. But Vance opposes helping Ukraine, spreads Russian propaganda about Ukraine, and is best known for yelling at Ukraine’s president in the Oval Office. On the base, Vance blamed the killing in Ukraine on Joe Biden rather than on Vladimir Putin, which is grotesque. Vance claimed that there is now an energy ceasefire in place between Russia and Ukraine; in fact, Russia violated it immediately. Russia is now preparing a massive spring offensive against Ukraine; the response of Musk-Trump has been to ignore this larger reality completely while allowing Biden-era aid to Ukraine to come to an end. Denmark, meanwhile, has given four times as much aid to Ukraine, per capita, as the US.