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More congressional Republicans are breaking a long-standing pledge to oppose tax increases before returning to Washington on Monday to avert a looming fiscal crisis with a deal that increasingly appears impossible to reach without changes to the tax code.

The decades-old pledge from the Americans for Tax Reform group has been signed by 238 House members and 41 senators in this Congress and has essentially become inescapable for any Republican seeking statewide or national office over recent election cycles, especially in the Republican-controlled lower chamber.

New York Rep. Peter King and Sen. Lindsey Graham said Sunday they would break the pledge and accept tax changes to generate more revenue to curb the trillion-dollar federal deficit.

Their statements followed a similar one Thursday by Georgia Republican Sen. Saxby Chambliss.

“I agree entirely with Saxby Chambliss,” King said on NBC’s “Meet the Press.” “A pledge you signed 20 years ago, 18 years ago, is for that Congress. …  The world has changed, and the economic situation is different.”

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The New York congressman said he was opposed to tax increases but that “everything should be on the table” when President Obama, House Speaker John Boehner and Senate Majority Leader Harry Reid try to broker a deal.

“I'm not going to prejudge it, and I'm just saying we should not be taking ironclad positions,” King added. “I have faith that John Boehner can put together a good package.”

Should Congress and the White House fail to reach an agreement, a $500 billion mix of federal cuts and unrelated tax increases would kick in January 2 -- the result of lawmakers failing to reach a more measured approach to cutting the deficit and keeping the country from going over the so-called “fiscal cliff.”

The across-the-board cuts to the federal budget would equal more than $1 trillion over the next 10 years.

Graham has suggested earlier that he would be open to changes in taxes, but repeated Sunday only if Democrats are willing to cut federal spending by scaling back entitlement programs like Medicare and Social Security.

“I will violate the pledge, long story short, for the good of the country, only if Democrats will do entitlement reform,” he said on ABC’s “This Week.”

He also said the only pledge that should be made when the country is trillions in debt is to “avoid becoming Greece.”

“Republicans should put revenue on the table,” he continued. “We don't generate enough revenue.”

However, Graham said he agrees with pledge champion Grover Norquist that tax rates should not be increases and instead suggested generating revenue through capping tax deductions.

Indiana Democratic Sen. Dick Durbin, on the same show, acknowledged that his party needs to “bring entitlement reform into the conversation.”

He included Medicare and Medicaid but argued Social Security should be kept off the table because it is a separately-funded operation that doesn’t add to the deficit. And he argued for tax increases for the country’s highest earners.

President Obama has suggested 10-year savings totaling roughly $4.4 trillion.

In addition, Arizona Republican Sen. John McCain said Sunday that he wants an approach similar to Graham’s -- closing so-called tax “loopholes” to raise revenue but no increases to the marginal tax rates.

"We can close a lot of loopholes," he said on “Fox News Sunday,” identifying deductions on charitable donations and on mortgage interest.