Eisenhower sent federal troops to Arkansas when the Governor refused to obey federal court orders to integrate the schools. I doubt Obama would be any more shy about using federal power.
I've thought of this too, the bad thing is if there was a Governor willing to defy the law, we'd have it on TV, Federal troops going to these areas and to the public at least, they would connect it back to the Civil Rights days, days of integration. I think a Governor who did so, though I would admire them for being brave would be at quite a bit of risk and in the end, the move looks like it would prove to be impotent.