House Speaker John Boehner said Tuesday he would introduce a bill extending tax breaks for all Americans making under $1 million, a Republican fall-back strategy in the event a \"fiscal cliff\" deal falls through. \"I believe it\'s important that we protect as many American taxpayers as we can, and our \'Plan B\' is to protect the American taxpayers who make $1 million or less, and have all of their current rates extended,\" Boehner told reporters after laying out his plan to the Republican caucus. \"Time is running short,\" Boehner\'s office quoted him as telling his caucus in a Tuesday morning meeting, referring to the year-end deadline to work out a deal or have $500 billion in taxes hikes and crippling spending cuts kick in. \"Taxes are going up on everyone on January 1. They\'re baked into current law,\" Boehner said. \"And we have to stop whatever tax rate increases we can.\" The strategy was swiftly rejected by the White House. \"The parameters of a deal are clear, and the president is willing to continue to work with Republicans to reach a bipartisan solution that averts the fiscal cliff,\" press secretary Jay Carney said in a statement. \"But he is not willing to accept a deal that doesn\'t ask enough of the very wealthiest in taxes and instead shifts the burden to the middle class and seniors. \"The speaker\'s \'Plan B\' approach doesn\'t meet this test because it can\'t pass the Senate and therefore will not protect middle class families, and does little to address our fiscal challenges with zero spending cuts.\" Obama, Carney said, remained \"hopeful that both sides can work out remaining differences and reach a solution so we don\'t miss the opportunity in front of us today.\" Democrats have long called for Boehner to bring a bill to the House floor that extends Bush-era tax cuts for households making under $250,000 per year, the cut-off point for President Barack Obama\'s tax hikes that he has demanded as part of any year-end deal to avoid the so-called fiscal cliff. But Obama offered a concession to Boehner on Monday, raising his threshold at which higher rates would come into force to households earning $400,000 a year and above. Boehner\'s office welcomed the narrowing of positions, but the speaker made it clear that there was no deal yet. \"What we\'ve offered meets the definition of balanced; the president is not there yet,\" he said. Boehner described the latest White House offer as including $1.3 trillion in new revenues, with $850 billion in net spending reductions. Asked what he wanted to see in an acceptable package, Boehner did not hesitate. \"I\'ve made it clear to the president that I would put a trillion dollars worth of revenue on the table if he were willing to put a trillion dollars of spending reductions on the table. That at this point would be my version of a balanced approach.\" While the White House has shown no sign it would accept the $1 million tax level, there is evidence it might have support from some Democrats, notably House Minority Leader Nancy Pelosi. In may she wrote Boehner a letter urging him to introduce legislation that maintained the middle class tax cuts. \"We must ask the very wealthiest Americans to pay their fair share,\" she wrote. \"Democrats believe that tax cuts for those earning over a million dollars a year should expire and that we should use the resulting revenues to pay down the deficit.\" Republican Representative Cathy McMorris Rodgers sounded optimistic Tuesday that an overall deal could be reached in time. \"The clock continues to tick and we\'re just days now from the end of the year,\" she said. \"And I think that the best Christmas gift that we can give America is an agreement, an agreement that gives certainty to our hard-working middle-class families as to what their tax rates are going to be.\" Boehner and Obama have engaged in fevered negotiations in recent days, including a face-to-face meeting Monday at the White House and a phone call later that night, in a bid to prevent tax hikes on all Americans and massive spending cuts from kicking in on January 1.