Florida already has 2 professional football teams. While it is probably large enough to support a 3rd, the other two teams in Forida would likely object to the idea as it would draw fans away from their fan base. LA would be a much better choice if a permanent move was to happen. However, I don't think the move would be permanent at this time.
San Antonio is likely one of the closest stadiums that is both large enough to hold a sufficient number of fans as well as close enough to New Orleans to still have a fan base. Displaced residents of New Orleans still could have a reasonable chance to see their team play. If it was in LA that would be almost impossible for most fans, and even something a little closer to home, like Oklahoma or Arkansas, still would be a considerable drive (not that SA wouldn't be). Another stadium under consideration is/was LSU's stadium. However it's in the midst of major renovations, has damage of it's own, contention with LSU's games, as well as lack of practice facilites for the Saints.
The Saints also have a little bit of history with San Antonio. They spent some time there when Ivan blew in...and team owner Tom Benson use to own a car dealership there. Not exactly major things, but still something that adds a little worth.