Also, the original statement is not quite correct - FDIC is funded by a special levy on all US banks, so while on principle it's backed by the "full faith and credit" of the US government, in actuality the money comes from the banking system itself.
Edit to add: from the article:
>The FDIC is funded by its member institutions through premiums and assessments paid on deposits. And, if ever needed, the FDIC can draw on a line of credit with the U.S. Treasury.
So, if you're a bank, you have to be a member of FDIC, or the banking regulators come and take your bank away. Being an FDIC member means you have to give them money, pretty much according to their whim (or they come and take your bank away). If that's ever not enough to fund a "not bailout", FDIC can get a loan from the Treasury, to be paid back from those premiums and levies on the banks over a period of time.
The banking system funds an insurance fund, but if that insurance fund is exhausted, the federal government is backstopping it.
There is no equivalent to a bank run risk on SS/Medicare so why put it in. Putting it in also means that these programs could cause massive inflation if the US Gov had to print money to finance them.