i think you might be out at one extreme end of the argument.
Federal firefighting forces go after fires in any state, and without a governor's invitation or declaration of disaster.
Mobilization across state lines is routine and instantaneous.
FEMA, as it was conceived, could do the same thing, but was managed by political hacks appointed by the president instead of dedicated, experienced, professionals.
Your worries about the military might be valid, i don't know, but i wasn't limiting the potential response to them. Like i said, a good leader would figure out how to get 'er done, and they didn't do it in a timely way.
Any way you slice it, the fact that we as a nation provide instant aid overseas yet turn things into a clusterfuck domestically does not really say much for our infrastructure of disaster relief.