BOCA RATON, Fla. — President Obama’s impending executive action on immigration is unleashing the fury of Republican governors who now control a clear majority of the nation’s statehouses — and not entirely for the reasons that partisans might expect.

The new legal protections that the president is poised to bestow on five million illegal immigrants Thursday will immediately thrust the issue back to the states, forcing dozens of governors who vigorously oppose the move to contemplate a raft of vexing new legal questions of their own, like whether to issue driver’s licenses or grant in-state college tuition to such people.

For Republican governors, the resentment is now as much operational as it is ideological.

The rapidly unfolding issue quickly overtook what was supposed to be a three-day victory lap here at a pink flamingo-colored resort where they have gathered for the annual meeting of the Republican Governors Association.

Instead of crowing about their electoral romp in the midterms, in which they captured 31 statehouses — the most since 1998 — the governors on Wednesday were bombarded by inquiries about how they would grapple with the practical and political repercussions of Mr. Obama’s action.