The Corps of Engineers knew that levees had broken by noon on Monday, August 29. They also knew that the city would eventually fill with water. Why FEMA and DHS was not informed will come out in the hearings.
Yes, state and local officials did dither. But Chertoff should have been mobilizing on Tuesday, August 30.
They may have been mobilizing since Bush declared it a disaster area. What I don't know and can't find out is what FEMA did during that time. It may be that they were simply incapable of reacting quickly to the exegency. Like a military unit caught facing the wrong direction.