Seeing as there are 250,000 small boats within 4 hours of New Orleans (to say nothing of 5,000 school busses) , not very long.
This goes on much longer and I think you'll start to see people frustrated by the lack of urgency of the local officials start to use those boats to save people. Just to the southwest (on higher and drier land) there are many good Cajun people with boats who I cannot believe will stand by and do nothing while they watch the innaction on television.
250,000 small craft mean nothing without communication, FUEL!!, and support.
"What we have here is a failure to communicate. I didn't want it this way. He wanted it this way. And, he got what he wanted".
It can sometimes take weeks to mobilize one platoon, with adequate support (nobody shooting at you, perfect weather).