As various chattering make-up jobs on television and radio express their opinion of the job done to help the victims of Katrina, it is sadly obvious that meny don't understand how things are meant to work. Many TV anchors do not understand even the basic points, so I will mention it briefly here.
Disasters, in terms of relief, have five stages:
 Preparation and planning
 First responders and evacuation
 Survival aid
 Restoration and rebuilding
The first stage is critical. Every group which means to help must plan for what they will do, in advance. The people staffed, their assignment and authority, the tools and supplies provided, all need to planned ahead of time. In the case of Katrina, the basic levels of planning were at the LOCAL, STATE, and FEDERAL level. All three levels had to work to be effective.
As for pre-positioning, in the case of Hurricane Katrina, the authorities understood that the weather would reduce mobility as soon as the storm hit, so supplies and personnel had to put in place ahead of the storm, during the critical window between alert of the storm and its initial impact.
The first responders have two main duties; get people away from danger, and perform life-saving tasks. This falls again on three levels - the LOCAl authorities, who have the most people on-scene at the start and who know the terrain and conditions best; the STATE authorities, who have better equipment and supplies; and the FEDERAL authorities, who have specialized equipment for critical situations, but who must be told by local and state authorities what is needed, and where.
Survival aid is set up at aid stations, and the critical issue here is coordination between the on-scene authorities and the groups bringing aid.
And finally, federal aid in disasters after the initial rescues is generally focused on financial and administrative aid, which is much different from the short-term material needs, which are generally addressed by the on-scene local and state authorities.
People will have different views of how each group did its job, but these simple categories help illustrate what went right, what went wrong, and why.