The Army Corps of Engineers is responsible for flood control in the region.
But you raise an interesting point. New Orleans is one of the places where the response to the melt-down of their city has been to build gated communities and get as far away from "those people" as possible.
Very much like the Third World.
People are free to live in a gated community if they choose to do so, but turning the rest of your city over to the criminals is a bad decision.
It wouldn't be the first time federal money money has been used to enforce apartheid. Chicago doesn't have a lot of levees, but it has expressways which were routed for the purpose of separating blacks and whites.