Perhaps people who are saying this are making the argument that a centralized body for responding to large-scale emergencies is the most efficient use of national resources and the most efficient mechanism for deploying those resources to places of need. But I think that many people who are saying this are making a simpler, and incorrect, argument: that the counterfactual to FEMA not existing to handle hurricanes is that there would be no resources to handle hurricanes.
Of course, that's not how this works. FEMA takes money to run. And the federal government can't magically generate that money; it has to tax and/or borrow to get that money. So really what FEMA is (and any federal government action, really) is the federal government taking a little bit of money from everyone and saving it for large-scale emergencies. That's money that could have been used for other purposes, including by individuals and by state and local governments to more directly prepare themselves for natural disasters.
Again, you can argue that centralizing this role makes perfect sense, and that would be a fine discussion to have. But you can't argue that either you have FEMA helping people or you have no one helping people. Everything has a cost, and the cost of FEMA taking money from all of us is that that money cannot otherwise be deployed. Every federal expenditure represents a transfer of resources from one group (all taxpayers) to another group (people in need of help in the midst of natural disasters). And every federal function represents the possibility of individuals and of state and local governments partially or fully absolving themselves of preparing to perform that same function.
Some roles really do make sense to be done centralized, and that justifies taking a little bit of money from everyone in order to provide for those roles. Bear in mind, though, that there are always unintended consequences. For example, one might argue that some parts of this country might build themselves out in ways that are physically dangerous, because they have the federal government as a backstop; take away that backstop, and more rational, environmentally sustainable land use patterns might emerge.
(A much older example dates back to the very earliest days of our country. After the Declaration of Independence, the US was still a fairly loose confederation of states. This made sense, since we were just emerging from under the rule of a tyrannical central government. The founding fathers started to push the young nation towards greater centralization. One piece of that was federal assumption of Revolutionary War state debts. Some states were fiscally prudent and weren't for federal assumption; others were deeper in debt and federal assumption seemed quite attractive. Virginia, land of Jefferson and Madison, was suspicious of centralized authority and had relatively low debt. In a grand compromise, they agreed to federal assumption if the nation's capital could be moved to closer to Virginia, in a swampland they called the District of Columbia. The pro-assumption northeners agreed, never thinking that mosquito-infested DC would ever house the federal capital. Of course, assumption worked in binding the nation together, DC became a viable capital location, and the story ended well. But at the time, the notion of a centralized federal government, and of federal assumption of state debt, was controversial. Some states could have argued that their fiscal prudence was being punished, because they were now sharing a federal government that was taking on others' profligate spending. And they would have a fair argument. My German readers are now sadly nodding their heads.)
I'm not arguing for the superiority of any of these lines of thinking. I'm just saying you have to play them out. There is no such thing as free government help, because it costs someone somewhere and takes resources away from other possible uses. You can quibble with Romney and others for not thinking that FEMA is a prudent use of the federal government's taxing power to fund a certain function, but it's not fair to say there's no upside to not paying for FEMA and no unintended consequences associated with paying for it.