I guess bringing it back would need some substantial pressure from both advocacy groups and states along the corridor, as it would add to Amtraks operating deficit.
Lining up a group of states that are very conservative and have shown very little interest in rail in recent years is not very likely. It is also quite understandable that they don't want to pay to get a service back that everybody else gets for free.
However the reason why Amtrak has kept it on suspended status instead of abandonment must be that there is some interest in reintroducing service one day. As someone has said it makes things a great deal easier with CSX and not less important it would probably also make it possible to restart service without a congressional mandate. Amtrak is prohibited to start any new service that loses money, but technically the Sunset East is not new - just on a very long suspension.
Now given the economic and political obstacles I would suggest an incremental approach to get things rolling. The most obvious (and missed) part of the route is probably the Mobile-Biloxi-NOLA corridor. What if Amtrak gave Misissippi and Alabama a really good offer, that might get them to get aboard anyhow: If you pay for a corridor train four days a week, we will extend the SSL to Mobile the remaining three - pay for four, get seven...
As I understand it enough equipment for both is sitting around in NOLA anyway, so the extension should cost a relatively limeted amount of money to run, if any could be found at all. And for Amtrak, ridership on the extended SSL will probably be better if it is part of a daily service, as that draws more local traffic. I have not looked into running times Mobile-NOLA, but the current schedule looks like providing pretty good departure times for a morning train westbound and returning afternoon train.
Granted this will not bring people to Florida right away, but I see several political gains. First it might up the pressure on the rest of the route so that a more railfriendly congress at some point throws in the extra money needed to support the full reinstatement. Second it will also put a spotlight on UP's ridiculousness on the western part of the route, when it comes to going daily, or if that still doesn't move the giant to make a payable slot for a full daily train, it might get Texas and Louisiana interested in doing a similar corridor four day fill in NOLA - SAS. Which brings me to the third and maybe most important gain. It will be the first state supported corridor in the deep South, arguably the most underserved region of the country today. The region badly needs examples of well working corridors that could inspire to more...