Washington ( CNN ) -- House Speaker John Boehner and other conservatives shot down a proposal from a senior congressional Republican who suggested that his GOP colleagues break from their firm anti-tax position and agree to a demand from Democrats to immediately renew middle-class tax cuts . Rep. Tom Cole of Oklahoma , a member of the leadership team that helps round up House votes , told fellow GOP lawmakers that he thought they should , as a matter of political strategy , extend just the tax-rate cuts for those making $ 250,000 or less before the end of the year -- a position being pushed by President Barack Obama and congressional Democrats . Cole first floated the idea at a closed-door meeting of the Republican whip team on Tuesday and his comments were first reported by Politico . Cole told reporters after another meeting on Wednesday with House Republicans that he believed giving certainty to the majority of American taxpayers now was important . But he emphasized that he still opposed increasing tax rates for upper-income Americans . `` In my view , we all agree that we 're not going to raise taxes on people who make less than $ 250,000 . We should just take them out of this discussion right now , continue to fight against any rate increases , continue to work honestly for a much bigger deal , '' Cole said . New Poll : Majority support taxing wealthier Americans . Cole added that major issues should be worked out in the debate next year . `` We need to deal with entitlement spending . We need to deal with job creation . Rates are intimately tied to that . So let 's have that discussion . But I think it 's easier to have without a lot of people whose taxes we do n't intend to raise being worried they might get raised . '' Cole 's Tuesday comments were reported and distributed broadly by Democrats as a major development in the fiscal cliff talks . But they were quickly rejected by Boehner , who is negotiating with the White House and Democratic leaders on a way to avert the combination of spending cuts and tax increases set to take effect without an agreement by year 's end . `` I told Tom earlier in our conference meeting that I disagreed with him , '' Boehner told reporters after meeting with GOP rank and file . `` He 's a wonderful friend of mine and a great supporter of mine but raising taxes on the so-called top 2 percent -- half of those taxpayers are small business owners that pay their taxes through personal income tax filing every year . '' At the Wednesday meeting in the Capitol , Boehner also made a point in his opening remarks to tell members he disagreed with Cole , according to two GOP sources who were in the meeting . CNNMoney : Fiscal battle over mortgage deduction . One of these sources said Cole brought up his idea with GOP members in the meeting , saying he did not support raising any rates . Conservatives immediately rejected Cole 's idea , and seemed annoyed that the attention on his comments was taking away from their focus to press Democrats to agree to some major entitlement reforms as part of a broad agreement to address tax rates and the automatic spending cuts . Idaho Republican Rep. Raul Labrador did n't mince words when asked by CNN about Cole 's idea . `` I think he 's wrong and I think most of the conference thinks that he 's wrong , '' Labrador said . `` I think he 's , you know , he 's a good man who 's served here for a long time . But he 's also a man who has voted for a lot of the increased spending in Washington , D.C. , and that 's the problem . '' CNNMoney : It 's time to fix the charitable deduction . `` I think this is a false choice between running off the fiscal cliff and damaging the economy , or raising rates on small businesses and professionals that also damages the economy , '' Texas Republican Kevin Brady , a senior member of the tax-writing House Ways and Means Committee , said . Cole said he would continue to discuss his suggestion with colleagues , and predicted that if it came up for a vote , it would pass the Republican-led House . But GOP aides made it clear there are no plans for any vote on a bill to separate the middle-class tax cuts from those for higher-income earners . Even though Republicans criticized the idea , Democrats praised Cole . Sen. Patty Murray , D-Washington , highlighted his shift in a speech on the Senate floor . `` I applaud Representative Cole for that common-sense and brave position . I am hopeful that he can persuade other Republicans to do the right thing for our families , small business owners and communities across the country who have so much at stake and who are looking to us to solve this problem , '' Murray said . Norquist 's no-tax pledge has survived challenges before . That kind of endorsement probably wo n't help Cole make his case with fellow Republicans . Asked about potential backlash to his idea from anti-tax groups focused on enforcing a `` pledge '' not to raise taxes , Cole seemed nonplussed . `` My job is to get the best deal from the American taxpayers that I can get , '' he said . `` If by keeping the pledge taxes go up on everybody , then I do n't know if that 's a very good idea . If , on the other hand , we can negotiate a deal , which I think we can , which keeps rates where they are but provides revenue and certainly protects people below $ 250,000 , I think we have a responsibility to try and do that . '' After the meeting with the rank and file , House Republican leaders were sitting down in the Capitol with several CEOs who are part of the `` Fix the Debt '' coalition chaired by Erskine Bowles , the former head of Obama 's deficit reduction committee . Boehner delivered a message to his members that he planned to reiterate to the CEOs , `` We wo n't be party to a deal that protects big businesses and preserves special-interest tax breaks while raising tax rates on the small businesses we 're counting on to create jobs . '' After the meeting Bowles told reporters he did not see the GOP showing any flexibility in their opposition to any tax rate increases .
Rep. Tom Cole floated idea of negotiating tax breaks for out earners over $ 250,000 . House Speaker John McCain and other conservatives reject his idea . Cole says major issues should be brought out in the House next year .