governors would fall into line pretty quickly

Dem governors would line up to oppose him.

This isn't really possible anymore, State NGs are nationalized so the federal government is already in charge. That's how JFK enforced desegregation in Alabama, he literally removed the state governor from the chain of command: https://en.wikipedia.org/wiki/Stand_in_the_Schoolhouse_Door

It's the same reason Walz did basically nothing in Minnesota. If he attempted to direct the NG or even his separate State militia, Trump would have thrown him into a charge under insurrection.

It would fall on the NG or Militia CO to proclaim allegiance to either the state or federal government. Considering what has happened so far, the most you'd see is some resignations.