I don't think waiting until the last minute to throw their hands up and scream "Run!" was very organizational. Where were the busses? They should know their own people well enough to know that too many couldn't run.
However, my being in New Olreans prior to this storm I can know the time line. On Friday afternoon the NWS's Storm Tracking Cone showed landfall anywhere from east of Panama City to the Texas Border. Furthermore, winds were at 110 MPH at noon on Friday. That was not a threat.
On Friday evening the mayor was on TV saying "Everyone needs to make a plan to get out of the city in case the storm heads to New Orleans. By Saturday morning the storm had intensified QUICKER THAN ANY STORM THAT HAD EVER BEEN IN THE GULF.
The Mayor held a press conference and said "This is the storm we have feared all of our lives. This is Not a Drill, Everyone needs to evacuate the city. Between Saturday morning and Sunday evening 1.25 million people evacuated the city. An evacuation on that scale had never been done in American History.
When you live on the Gulf Coast you learn that it is best to evacuate BEFORE THE HURRICANE and interestingly 1.25 million people were able to do all without any help from the Fed.