"I think that lifting the FDIC insurance cap is a good move," Senator Elizabeth Warren, a Democrat, said on CBS's "Face The Nation" program, referring to the Federal Deposit Insurance Corporation's current $250,000 limit per depositor.
"What I will do though, legislatively, and in an oversight function, is to determine whether or not we need to address the FDIC deposit level," McHenry told the same CBS program.
During the financial crisis that erupted in 2008, the FDIC temporarily backstopped all deposits to safeguard smaller banks.
Pressure on midsized and smaller banks from deposit outflows continued on Friday despite a move by several large banks to deposit $30 billion into First Republic Bank, an institution rocked by the failure of Silicon Valley Bank and Signature Bank.
McHenry said he wanted to examine the trade-offs of higher deposit insurance limits, "the moral hazard of having more risk-taking in the financial sector, and also the impact it would have on community banks."