"One approach is to define government as the decision-making arm of the state, and define the latter on the basis of the control it has over violence and the use of force within its territory. Specifically, the state (and by extension the government) has been considered by some to be the entity that holds a monopoly on the legitimate use of force within a territory."
I think this definition of government provides a context that is useful in understanding the Federal response to Katrina. The government lost immediate physical control over a part of it's real estate and so it took it back in a military operation.
The government's priority was to reestablish it's monopoly on the legitimate use of force within the territory.