As Congress prepared to dive back into \"fiscal cliff\" talks on Monday after the Thanksgiving holiday, there were encouraging signs that Republican intransigence on tax could be easing. For the second time in days, a leading Republican, this time Senator Lindsey Graham, edged toward violating something that had been sacrosanct -- a longstanding pledge signed by many in his party never to raise taxes. Strings were attached -- concessions by Democrats on social welfare programs like health care for the elderly. But his change of heart was a hopeful sign that the Republican leadership is ready to make tough choices in order to strike a deal. Both Republicans and Democrats are well aware of the need for the country to get its fiscal house in order, as America tries to rein in a huge debt that has been growing bigger by the day and reduce deficit spending. If no deal is reached before the end of the year, a poison pill law of tax hikes and massive spending cuts, including slashes to the military, comes into effect with potentially catastrophic effects for the fragile US economy. After months of stalemate, congressional leaders met on November 16 with President Barack Obama -- who is deemed to have a considerably stronger negotiating hand after handily winning re-election 10 days earlier. Just five weeks now remain in the calendar year to conclude an agreement before the expiration of tax cuts put in place during the presidency of Obama\'s predecessor, George W. Bush. Obama has said that any deal he concludes would have to include an increase in taxes on wealthy taxpayers, something congressional Republicans so far have rejected. The plan he proposes -- and presented to voters on the campaign trail -- would raise the tax rate for top earners, but keep Bush-era tax rates for individuals who make less than $200,000 per year and families earning less than $250,000. Republicans insist raising taxes on the wealthy would be counter-productive and only serve to slow economic growth and ensure that the country continues to be plagued by economic stagnation. They insist that higher taxes would dampen spending and hiring and investment by business owners. The top income tax rate, which now stands at 35 percent, will automatically revert to 39.6 percent at the beginning of 2013 unless there is a new budget deal. Republicans say they prefer to look at ways to bring in more tax revenue by completely overhauling the old and unwieldy US tax code, including closing what they say are \"special interest loopholes\" likely to hit the poor and the middle class as well as the rich. Graham, speaking Sunday on ABC\'s \"This Week\" program, said it was fair to ask his party to do this in turn for Democratic concessions on reducing government spending on social welfare programs, known here as entitlements. \"When you\'re $16 trillion in debt, the only pledge we should be making to each other is to avoid becoming Greece, and Republicans -- Republicans should put revenue on the table,\" Graham said. He was alluding to Grover Norquist, a powerful conservative political player in the US budget debate, who over the past two decades has persuaded many Republicans to sign a pledge not to raise taxes. \"I want to buy down debt and cut rates to create jobs, but I will violate the pledge, long story short, for the good of the country, only if Democrats will do entitlement reform,\" Graham said. Graham\'s apparent willingness to ignore the no higher taxes pledge came just days after another prominent US senator, Saxby Chambliss, said he would not be not bound by the promise either. \"I care more about my country than I do about a 20-year-old pledge,\" Chambliss said. Economists have said that closing loopholes and ending deductions will likely not generate sufficient money to chip away at the national debt, and that a combination of tax increases and spending cuts will be needed. Speaking on the same program as Graham, Democratic Senator Dick Durbin insisted that tax rates for the highest earners do have to up. \"How in the world are you going to reduce deductions and generate enough revenue for meaningful deficit reduction,\" Durbin said. Some experts said that there need not be a \"grand deal\" by the end of the year, because they could give themselves an extension by passing new legislation. \"Anytime Congress puts handcuffs on itself, it still has the key to those handcuffs. It can open the handcuffs anytime they want, or say. \'OK, we\'ll change the lock\',\" said Roberton Williams at the Tax Policy Center, an independent think tank.