WASHINGTON, Nov. 25, 2012 -- With the fiscal cliff looming for the United States, some Republican members of Congress said today they are ready to break a long standing pledge not to raise taxes.

"The only pledge we should be making to each other is to avoid becoming Greece. And Republicans should put revenue on the table," South Carolina Sen. Lindsey Graham said on ABC's "This Week."

Read more of the discussion of the fiscal on "This Week" today.

Graham's comments followed those by another Republican senator, Saxby Chambliss of Georgia, who said last week he'll no longer abide by the pledge.

"I care more about my country than I do about a 20-year-old pledge," he said in a local interview.

He got support today from House member Peter King, another Republican from New York.

"I agree entirely with Saxby Chambliss -- a pledge he signed 20 years ago, 18 years ago is for that Congress," King said on NBC's "Meet the Press." He added, "The world is changed and the economic situation is different."

Read Matthew Dowd's analysis of the efforts to avoid the fiscal cliff.

This growing chorus is about the pledge that Americans for Tax Reform president Grover Norquist has gotten hundreds of Republicans to sign. But in an interview with ABC News, Norquist says it's just a few deserters.

"The people who have made a commitment to their constituents are largely keeping it," he said. "The fact is there is more support for both protecting the rates, you saw the Republican leader in the house say rates are non-negotiable, and he also talked about revenue coming from growth."

But President Obama has said rates will go up for the wealthy. There could be some political cover for Republicans if the country actually goes over the cliff. All the Bush era tax cuts would expire, including those for the wealthy. Congress could then vote to actually reduce taxes for everyone expect the rich. Therefore, they wouldn't technically raise taxes and violate Norquist's pledge.

But Nordquist said he doesn't think the public would buy those political moves, and he also doesn't think the country will actually go over the cliff.

"I think we'll continue the tax cuts. Not raise taxes $500 billion. Obama made the correct decision (by extending the Bush tax cuts) two years ago," Norquist told us.

Leading Democratic Sen. Richard Durbin also said he believes a deal is possible now that the Thanksgiving holiday break is over.

"We can solve this problem," he said on "This Week," adding: "There's no excuse. We're back in town."