Federal Deposit Insurance Corp. head Sheila Bair "has indicated there are problems" with other banks, said Sen. Chris Dodd, D-Conn., in an appearance on CBS' "Early Show," The Hill reported.

Dodd said he is "more optimistic" about mortgage giants Fannie Mae (NYSE:FNM) and Freddie Mac. (NYSE:FRE)than he is about some lenders that engaged in these "very, very bad mortgages."

IndyMac's collapse is the second-biggest bank failure in U.S. history.

To help quell fears on Wall Street about more bank failures, the White House Sunday announced a plan to help out mortgage giants Fannie Mae and Freddie Mac.

U.S. Treasury Secretary Henry Paulson said he would seek congressional authority to increase the two companies' lines of credit with the Treasury and also seek approval to allow the Treasury to buy equity in Fannie and Freddie if needed.