It is absurd to expect a city government, burdened with mostly poor citizens and very little tax base, to deal with such a disaster. The money for such massive responses must come from where all the money is - the owning classes.
It isn't exactly a "poor" city overall. They did have a relatively strong tax base. There was huge development downtown, massive public projects. There was also a fairly strong middle class and a lot of incoming money from tourism.
This one isn't a political issue, more of an engineering one. The 17th Street Canal Levee, that broke, was "upgraded" 5 years ago. There were both federal (the bulk) and local contributions to its building.