There would be tripwire forces located in Greenland. The US would likely be required to directly engage European troops. I would expect Europe to let the carrier know it got no chance before it even starts shit, in the above scenario. Like when the US under Biden surfaced a nuclear triad sub in the Baltic Sea to dampen Russia's nuclear threats against Europe, early in the Ukraine war.
Not sure Europe could afford to abstain from a military response after being actually attacked. It would look extremely weak, disrespectful to their attacked/fallen troops and puts their military deterrent in question globally. You can wreak the economy only once cutting ties with the US and it got more impact domestically with a costly war starting. To deescalate, US society's pain expectations must max out immediately, before the people, media and economy can adapt to a new normal/narrative. Look at Ukraine, a slow, reluctant response makes everything worse. If Europe/US had maxed out their support immediately, Russia would have like pulled out. Years of extreme pain must be the message, another costly war dragging on forever, something Americans understand and feel tired of.
And I presume Canada would also not be too pleased, potentially having to up the stakes for a war in their neighborhood. A war which may just as well have fallen onto their own soil. It would be wise for them to stand with Europe, if they want to keep their own independence.
The US military leadership actually having to plan an all-out war with Europe, possibly Canada, may prompt some introspection and a chance for internal conflict. Rumor has it, behind the scenes, the US NATO generals already apologized to their European counterparts for Trump's remarks on Greenland. There is probably a non-zero chance, any attack order would cause a coup rather than a war with Europe. Domestic revolt will only happen, if such conflict is credibly the stupidest thing imaginable on every axis and when relevant actors are actually confronted with that reality.