It won't, precisely because New Orleans already has many places below sea level. It's got a head start.
It's spent billions of dollars over 100+ years making the outer boundaries water tight, and building the infrastructure to support all of that, including the ability to pump 100% of rainfall out.
To New Orleans, the cost of any sea level rise has essentially already approached the marginal rate.
No where else in the world, with the exception of probably the Netherlands, is better prepared for rising waters, whether it's storm surge or sea level rise.
Everywhere else has to pretty much start from scratch.
The post-Katrina improvements have combined the patchwork systems into one.
The improvements should have been made long before Katrina, but the corps of engineers stalled most attempts, and Congress refused to let the corps do anything without direct Congressional funding, which never came. Until Katrina.
People aren't currently avoiding New York because of sea level rise. And are spending far greater amounts on business investments there.