FEMA did not hand over reins of authority. The state....any state, including Louisianna is in charge from the get go. State's rights. If a situation becomes so out of control that the state cannot handle it, then they can REQUEST assistance from the appropriate federal agencies.
Generally the agency the Governor will first go to is the National Guard in their state. The guard does not have policing authority, but they can do rescue etc.
FEMA is not a rescue organization, it is not a first responder organization. It is an organization that works to coordinate agencies such as the Red Cross, all the faith based organizations, volunteers etc. to provide relief, rebuilding etc.
The Governor of Louisianna and the Mayor of New Orleans messed up from the get go. It took President Bush personally calling them to even get them to issue a mandatory evacuation. But even when they did that, they did not follow their own plan, which was to use the buses to get people out of town that could be taken out, then the superdome was ONLY to be refuge for those who were too affirmed to leave via bus. Instead they basically sent everyone to the superdome, telling them to take food and water with them, also blankets etc.
Nagin's power never extended beyond his jurisdiction, which means he had the legal ability to shuffle deck chairs within the Titanic.
http://www.legis.state.la.us/lss/lss.asp?doc=85673