When the FDIC exhausts its own funds, any other claims are put to the U.S. Government and become an obligation of the FedGov.
The govt would like you to believe that but in reality the obligation goes to the taxpayers.
That is the worry. The US dollar is going to be toast, who would want it?
Here is an interesting read, old but still relevant.
http://www.freerepublic.com/focus/news/2051250/posts?page=1