Close to two weeks. That was the result of Hurricane Katrina. When my wife was a young girl, living in New Orleans, Hurricane Betsy took out power for about three weeks if not longer.
It is not the end of the world, but when temperatures are in the 90s and ice is hard to find, it does become trying. The hardest part is trying to sleep. You have the windows open to catch any breeze you can, but you have to listen to all the noises, the most irritating of which is the noise of all the portable generators people are running throughout the night.