As a regulator, FDIC supervises state-chartered banks that aren't members of the Federal Reserve system—that is, smallish banks that played little or no role in igniting the financial conflagration of the past couple of years. It also takes over and shuts down or sells off troubled banks supervised by other regulators such as the Fed, the Office of the Comptroller of the Currency, and the Office of Thrift Supervision—but it's those other regulators that are supposed to tell it when there's trouble.
The reason the FDIC might soon have to borrow some money is because banks are caught up in their worst crisis since the 1930s. It was in the 1930s, of course, that Congress created the FDIC with the intent of heading off bank runs by insuring that small depositors wouldn't lose their money. It's been hugely successful in that; the problem is that we allowed the creation of a shadow banking system of securitization, money market funds and investment banks that was outside the FDIC umbrella and turned out to be pretty susceptible to bank runs. There's lots of blame to go around for letting this happen, but not very much belongs with the FDIC.