Fiscal cliff: Republicans start to line up behind compromise with Barack Obama Mr Corker urged Republican negotiators to accept this in return for deeper cuts to schemes such as Medicare, the health care scheme for elderly Americans, than the $350 billion offered by the president. "A lot of people are putting forth a theory, and I actually think it has merit, where you go ahead and give the president the two per cent increase that he is talking about, and all of a sudden the shift goes back to entitlements," he said. Mr Corker became the fourth Republican Senator to warn that the party must strike a deal or risk being seen as holding the US economy hostage in order to protect the richest Americans. He was joined by Tom Coburn, a Republican Senator for Oklahoma, who on Sunday night reiterated his desire for Republicans to "accept a tax increase as a part of a deal to actually solve our problems." Mr Obama, who won re-election after campaigning relentlessly on a promise to raise taxes for households earning more than $250,000 a year, has asked for $1.6 trillion (£1 trillion) in new tax revenue over the next decade to help reduce America's annual trillion-dollar budget deficit. Yet Republicans, many of whom pledged never to increase taxes when arriving in Washington, kept control of the House of Representatives. Their opening offer in the crisis talks allowed for only half as much new revenue as Mr Obama's - and for it to be raised by merely closing loopholes in the tax code. In an indication of a possible shift towards a compromise, Mr Boehner on Friday declined to rule out a new 37 per cent tax rate. "There are a lot of things that are possible to put the revenue the president seeks on the table," he said. Tom Cole, a Republican senator for Oklahoma, said yesterday that party leaders needed to recognise that Mr Obama had the stronger hand because taxes would rise on January 1 even if no deal were struck. "Some of our people think if we dig in and hold strong we can stop it, but that's not the case," Mr Cole told CNN. It happens automatically. He, too, urged Mr Boehner to recognise that they only held control over one chamber of Congress, and to strike an agreement in which the party won deeper cuts to expensive public spending programmes. "You have to do something, and doing something requires the co-operation of the Senate, which the Democrats run, and the signature of the president," said Mr Cole. So we're not going to get 100 per cent of what we want.