That would definitely do it. With the way Trump is talking Denmark might end up being forced to expel the US military from Thule to avoid a Chrimea scenario.
What even happens if one NATO member attacks another? Does the aggressor immediately get their membership nullified and the rest must come together and declare war on them?
NATO immediately loses all credibility. Otherwise, nothing much.
NATO was founded as a defensive pact against the Soviet Union.
The only time it was ever used was as a tool by the US to force other countries to join the war in Afghanistan.
Article 5 isn't an automatism that forces all members to start an all-out war. They're still sovereign.
Intra-alliance fighting has always been a concern because of Greece and Turkey. Article 5 is probably the only reason they haven't already gone to war. But yeah the US would fight all of European NATO that answers the call, win a pyrrhic victory, and destabilize Europe for the next 100 years.