An incredible overview of the problem was written 20 years ago by John McPhee[1], as part of his book "The Control of Nature". Unfortunately, solving the problem in the long term means essentially undermining the entire economy of South Louisiana, and leaving the City of New Orleans destitute.
I served in Baton Rouge for 3 years and spent a lot of time on the Mississippi River. It's an extraordinary resource that much of America silently takes for granted. I with there were better solutions to save it and protect the people of Louisiana, but I don't feel like I have better answers to these questions that anyone else. It's a tough situation.
[1]: http://www.newyorker.com/magazine/1987/02/23/atchafalaya
It's the parts of the delta which are fed by the Old Mississippi which are disappearing, and this is a totally natural process. The same river is what serves the port of New Orleans. The natural course of the river can only be temporarily stayed; it will find a way around the ORCS eventually. If the river is allowed to flow naturally, the majority of Southeast Louisiana, including New Orleans and Lake Ponchartrain, will disappear under the ocean.