It was only a matter of time before Romney flipped again. But in this case, Romney is having to back-track a lot. Since the Primaries, Romney has held strong in his belief that things like disaster aid should be kicked back to the states and, whenever possible, should be handled by the private sector. It is his belief that this will make responses to disaster faster, cheaper, and better. Romney even said it was "immoral" for disaster relief to be handled by the federal government.
Here's just a few issues with that. If it's handled solely in the private sector, who pays for it? Individual citizens? If that's the case, who is responsible for infrastructure repairs? Does the state pay? If so, how is that cheaper since a private business would be charging enough money to make profit on top of their operation costs, whereas a state government would simply pay the workers?
Then, there's the question of sending it to the responsibility of individual states to begin with. Sure, it would mean less money being spent by the federal government, but it would also mean a greater strain on state and local governments. It would mean more slower responses, less coordination, and no ongoing support except with state and local tax dollars for victims. I know my state couldn't possibly pay for all of the recovery needed on its own without severe tax hikes and spending cuts on everything else. They would have to do nothing else except disaster recovery for a year or more.
For these reasons, I think that Romney is wrong to suggest that FEMA should be a state's issue. Of course, you can't expect him to really get it; he only recently decided, again, where he stands on the issue.