The way I remember it, there were federal resources available for New Orleans immediately, but the mayor and governor had to request them as required by law. They didn't. Bottom line is that the poor Katrina response is due to local and state incompetence (including the squandering of federal money that had been intended for fortifying the dikes that eventually broke). When FEMA did start to act, they did more than is being done now. For example, places to live, relocation services, reliable fresh water, etc. If anything it was comical how much they did, and how much of it was ineffective.
Bush was a pretty bad president, but I think he's been unfairly blamed for the Katrina response. It's become clear that blaming Bush for that was a political narrative intended to make him look bad to minorities, and it worked.
There was no martial law, but there were curfews intended to reduce widespread looting.