Earlier quoted context omitted.
Trust me, Denmark wasn't posturing. The assumption was - and still is - that the USA wasn't posturing either. We (and I realize I obviously don't speak for all of Europe but I have my finger on the pulse in many places here) are also not assuming that when Trump is gone the USA will go back to normal.
This is absurd in the extreme. In actual war there is absolutely no possibility of success for Denmark, even with the help of allies. Failure to capitulate results in nothing but death and destruction with no hope of strategic gain to begin with. What you are likely experiencing is a modern belief that screaming and shouting will bring popular diplomatic pressure to bear on the opponent, thus arresting their actions.…
Assume that Denmark's strategic success criteria is not "win up-front battles with US armed forces". And that they understand the difference between "lost battle(s), got occupied" and "nation permanently removed from existence".
Also, US service members are not slavishly loyal Clone Troopers. That I've heard, the greatest fear of most senior American officers is that the CIC will issue orders sufficiently offensive to the lower ranks that they will be disobeyed at scale.