It doesn't do anyone any good to just dump thousands of military personnel in an area without the necessary logistics support (food, water, supplies, etc.).

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A disaster of this scale represents huge logistics challenges. Both of New Orleans' main airports were closed due to flooding. Many roads and railroads were closed due to flooding and debris. Fuel is in short supply, so it has to be brought in along with everything else.

Hasn't our military been reorganized over the last decade or so to provide for rapid-response? Isn't an ability to deliver supplies and logistical support along with troops an integral part of rapid mobilization plans? Surely we're not dependent on existing infrastructure like airports and rail lines; and we have the means to bring in our own fuel. The basic problem doesn't seem fundamentally different from responding quickly to a military situation, and supply lines are certainly much shorter inside the US. So, I guess I don't understand why the obstacles should be as daunting as you describe.