For more detailed information on the FDIC see this article:
FDIC May Need $150 Billion Bailout as More Banks Fail
FDIC's Secret List
The FDIC knows which banks are at risk; it has a watch list with 117 institutions. The agency won't disclose their names because doing so could cause depositors to panic and pull out all of their funds.
It won't take many more failures before the FDIC itself runs out of money.