Democrats have welcomed what they say are the first cracks in the Republican party's long-standing opposition to any tax rises, which Barack Obama has insisted must be part of a deal to resolve the fiscal cliff crisis.

But anti-tax campaigner Grover Norquist, a key figure in the negotiations, predicted that Republican members of Congress would not back down and insisted he would hold them to pledges most of them signed not to raise taxes.

In an interview with the Guardian, Norquist, president of Americans for Tax Reform, was scathing about a small group of Republicans who hinted over the weekend that they might break that pledge in order to resolve the crisis.

Over the last 48 hours, senators Lindsey Graham and Saxby Chambliss and congressman Pete King have said they do not feel bound by the Norquist pledge they signed.

Members of Congress returned to Washington on Monday after the Thanksgiving holiday with time running out to resolve the crisis before the 1 January deadline. If no deal is reached, all taxpayers will face rises and huge across-the-board cuts will be implemented, including military and welfare spending.

Norquist portrayed the three Republicans who have broken ranks as being the usual suspects, not representative of the party at large and over-fond of appearing on television.

Norquist, who is a central figure in the fiscal cliff negotiations, predicted these members of Congress did not mark the start of a stampede by Republicans in Congress.

He predicted the Republican coalition against tax rises – the majority of Republican members of Congress have signed Norquist's pledge not to vote for an increase – will hold fast.

"One cannot see into the future," Norquist said. "But in 2011 the same people were saying the same thing. The Republican party held and the leadership held."

The promise is one of the biggest stumbling blocks to getting Republicans to support any fiscal cliff deal involving a tax rise.

President Obama is insisting that as part of a tax and spending deal to prevent America going over the 'fiscal cliff', taxes for the wealthiest need to rise.

Democrats welcomed the comments by Graham, Chambliss and King as offering hope of a deal.

Dick Durban, a senior Democratic senator, said: "Let me salute Lindsey Graham. What he just said about revenue and taxes needed to be said on his side of the aisle."

Graham, on ABC, said: "I will violate the pledge, long story short, for the good of the country, only if Democrats will do entitlement reform."

Chambliss told a Georgia TV station: "I care more about my country than I do about a 20-year-old pledge." He added: "If we do it [Norquist's] way, then we'll continue in debt."

King, on NBC, concurred, saying: "A pledge you signed 20 years ago, 18 years ago, is for that Congress. … For instance, if I were in Congress in 1941, I would have signed a declaration of war against Japan. I'm not going to attack Japan today. The world has changed, and the economic situation is different."

Norquist said the views of these three were not new and the same views had been expressed during the 2010 and 2011 congressional stand-offs.

"First of all, the three said the same thing two years ago. They are trying today to start a stampede over the debt ceiling."

He added: "These are three guys who like television. But that has not in the past translated into the rest of the party voting with the guys who want on television. Could it happen? Yes. Does history suggest it will happen? No."

Norquist began his no-tax-rise pledge more than two decades ago and has collected the signatures of the bulk of Republican members of Congress.

The pledge says they would "oppose any and all efforts to increase the marginal income tax rates for individuals and/or businesses".

Norquist said: "They have made a promise to constituents. If they break it, they can have that conversation with their constituents. It is like someone who cheats on their wife."

He described the three as having "impure thoughts" but noted that they had not yet acted on them and were only saying they might vote for tax increases. "They might also shoplift, or might rob a bank," Norquist said.

He proposed that during the negotiations C-Span be allowed to cover the behind-closed-doors negotiations and that once a deal is reached, it be printed and made available to the public for seven days before a vote.