You are correct, according to this wsj article, and that would be a very scary situation. If the FDIC can’t cover the bank failures then I’m almost certain the reaction would be monetization. In which case your dollars will be about as useless as if they had been lost anyway.
If this situation makes you panic then I would consider getting into a bank which is fdic or ncua insured but which doesn’t have a lot of exposure to the mortgage meltdown. Of course, when the FDIC needs more money they’ll raise the rates they charge banks for insurance, so all banks will suffer (and undoubtedly pass the cost on to the consumer).
If there’s a run on the banks, all bets are off.
Disclaimer: I am not in the banking industry. I just read a lot and I am very interested in what’s happening to my money. I’m not trying to give advice, just trying to get feedback on things I’m considering doing for myself.