Updated

The fiscal negotiations in Washington continue to divide congressional Republicans who now appear in the position of having to agree to some measure of tax increases to generate revenue to reduce the federal deficit.

Taking a pledge not to increase taxes has long been considered almost a prerequisite for Republicans seeking a congressional seat -- with roughly 90 percent of senators and House members in the 112th Congress having taken the one issued by Washington-based Americans for Tax Reform.

How powerful is the pledge, which the group has issued for the past 26 years?

Group founder Grover Norquist said that now-wavering Sen. Bob Corker was elected to the Senate on the strength of signing the pledge.

"He would not be a senator today if he hadn't made that commitment,” Norquist told Fox News earlier this week.

Still, Corker and others who have recently made a public display of disavowing the pledge find themselves at odds with party members showing solidarity to it, and moreover, fiscal conservativism.

On Monday, Sen. Mike Lee, R-Utah, acknowledged that more revenue is needed to reduce the estimated $16 trillion deficit but concluded “raising (tax) rates will not help with that.”

Lee was joined at a Capitol Hill press conference by 2012 Republican presidential candidate Rick Santorum, a fellow conservative who also opposes a tax-rate increase.

John Brabender, Santorum’s longtime political strategist, later told FoxNews.com he thinks some conservative Hill lawmakers are being driven to the center as a result of the elections three weeks ago in which Democrats essentially did better than Republicans.

“We have to increase revenue,” Brabender said. “But I hope the party takes a deep breath and remembers our beliefs. … Raising taxes slows the economy. It’s counter-intuitive. Lots of Republicans think the solution is to act every inch like a Democrat.”

Republicans must in fact decide on two tax issues as they negotiate with President Obama and other Democrats on a way to avert a $500 billion mix of tax increases and severe federal-spending cuts before they kick in  Jan. 1.

The first is whether to increase taxes -- or at least eliminate some tax loopholes -- to generate revenue to trim the deficit. The other is whether to accept the president’s offer to extend Bush-era tax cuts, but only for families earning less than $250,000 annually, which is roughly 98 percent of Americans.

Oklahoma Rep. Tom Cole, a conservative and member of the House whip team, appeared willing last week to accept the deal and first made his case Tuesday in a closed-door meeting, where he reportedly received some measure of support.

“If we don't believe taxes should go up on anybody, why can't we accept a deal that takes 98 percent out and still leaves us free to fight on the other grounds," he later said, as reported by Politico.

The plan was almost immediately rejected by House Speaker John Boehner who has instead proposed closing some tax loopholes as a way to generate revenue.

“I disagreed with him,” Boehner said.