In an appearance on ABC's "This Week" program, the South Carolina Republican said while the notion of nationalizing the country's banks is "not comfortable," he said it might be necessary.
"I think we have gotten so many toxic assets spread throughout the banking and financial community throughout the world that we're going to have to do something that no one ever envisioned a year ago, no one likes," Graham said.
Appearing on the same program, Sen. Charles Schumer, D-N.Y., said he isn't in favor of nationalizing banks.
"I think government is not good at making these decisions as to who gets loans and how this happens," Schumer said.
U.S. Rep. Maxine Waters, D-Calif., said "the word nationalization scares the hell out of people" but the debate it has triggered is good.
"I don't think that we are ready to move to the point of a formalized nationalized banking program yet," she said.
Waters said Citibank is "probably almost nationalized" given the amount of federal bailout funds it has accepted.