The Federal governments job in Katrina was to help New Orleans by sending troops and FEMA. They didnt do a good job at that because the troops arrived six days later while people died and the head of FEMA lied to the press saying he learned about the disaster too late.
The State governments job was to inform the Federal on what the state needed from them, but with a lack of communication that really didnt turn out well.
The local goverments job was to atleast try to get people out of the state. But with most public transportation down that was nearly impossible.