A Republican senator said Sunday "it's fair to ask my party to put revenue on the table" as part of the solution to avoid the looming automatic tax increases and across-the-board spending cuts known as the "fiscal cliff."

South Carolina's Lindsey Graham said he's "willing to generate revenue" by steps such as capping tax deductions, which he says would most affect upper-income Americans. But he says he won't agree to higher taxes - a position shared by most Republicans in Congress.

President Barack Obama wants to let tax rates rise for wealthy families while sparing middle- and low-income taxpayers.

Graham told ABC's "This Week" that "for the good of the country," he's ready to violate an anti-tax pledge followed by most Republicans if Democrats agree to big changes in entitlement programs.

Rep. Peter King, R-N.Y., said a pledge signed years ago should not necessarily apply in economic conditions that have changed greatly.

"I think everything should be on the table," he said, adding "I'm just saying we should not be taking ironclad positions."

King said on NBC's "Meet the Press" that "we have to show the world we're adults. The election's over." Get Obama and the congressional leaders in a room, he said. "That's what representative government should be about. No one gets all their way."