Hmm, as it happens there have just been general elections in Greenland [1]. Share of vote of parties that support independence: Pretty much 90%, with big gains for the party that advocates a "more rapid independence", and "favors greater cooperation with the United States". So perhaps Trump's bluster has produced effects... If perhaps not what Denmark would like.
The party gaining most this election has a stance of "remaining within the Danish Realm for the foreseeable future, with independence as the end goal of a gradual process that starts with increased self-determination".
Yes, the party that came first and gained a lot is pro-independence.
The party that came second and gained a lot, too, is also pro-independence but more rapid with better relations with the US, as mentioned, so it seems that Trump's bluster has influenced things but perhaps not the way Denmark would like to...
When the debate effectively shifts from "should we become independent" to "how quickly should we achieve independence" (i.e. not "if" but "how") then I'd say that it's going well for the US and badly for Denmark, despite the European news coeverage.
Overwhelmingly, they want to be Denmark. And are Denmark. And see USA as a threat now.