I think there are several misconceptions here
regarding the concept of just moving thousands of troops in.
First, the military is not a giant "meals on wheels" program. They are there to kill and destroy stuff. When folks talk about moving troops in (Regular Army), we're most often talking about infantry. While infantry can do basic law and order stuff, it's not really their mission and they're not that good at it. Again, it's there to kill and blow stuff up, not hand out pampers.
Second, some here seem to think that regular Army troops (again, infantry primarily) are just sitting around eating cheetos all day with nothing else to do. Nothing could be further from the truth. They spend almost all of their days training, sometimes out in the middle of nowhere on a base for days, maybe weeks at a time. They're not incommunicado but you can't just have them stop on a dime and jump on a plane. It doesn't work that way.
Third, the same thing goes for aircraft. They're committed to other missions and not just lounging around doing nothing all day. Some of these missions are vital to U.S. Security issues and cannot be diverted. Believe it or not, it takes some planning.
Fourth, from what I understand, the airport in NO is a total mess with debris all over the place and a good bit of water on the runways. For the most part, it's not usable at this point and that makes a HUGE difference if you can't land fixed wing aircraft on it. Until it's cleared and the water drained, it's not much use.
Do I think more can be done? Probably but I think it's grossly inaccurate to assume we could have 250,000 troops in there overnite.