I've seen a similar dynamic play out in academia a bunch of times. Basically, lots of people support the idea of bringing in some hard-nosed administrator who's going to kick a bunch off asses and get the place into shape. Of course, everyone imagines that it's other peoples' asses that are going to be kicked, and they are then shocked to discover that maybe it isn't such a good idea to put a clueless authoritarian asshole who gets a kick out of causing pain in charge of things.
And so it is with Republican governors.
