Would the governor or a federal official ask adjoining state governors to provide additional helicopters?
Just a guess, I would think the Governor first, after getting an update/request from the Mayor. The Governor is tucked 60 miles away in Baton Rouge and would need an update from the Mayor.
The brunt of the hurricane had not yet reached New Orleans when the flooding started.
Until the hurricane had fully passed, it would have been impossible(safety first) to get anyone in there.
It was a major snafu, no doubt. New Orleans will be used as a case study for many years to come.