The localities rely on the states and the states are the ones doing the cutting.
Note that places like Texas were affected much less by the housing bust than other states and yet still went through with austerity. This is a systematic problem among the GOP believing they have to cut spending across the board. I do put more blame on the federal gov't, of course, but the other aspects can't be ignored.
I don't think we should dismiss that these GOP states are the ones driving state cuts compared to the other states because it's the economic problem of the party itself.