WASHINGTON — Senate leaders and their aides sought a formula Saturday to extend tax cuts for most Americans that could win bipartisan support in the Senate and final approval in the divided House by the new year, hoping to prevent large tax increases and budget cuts that could threaten the fragile economy.
As part of the last-minute negotiations, the lawmakers were haggling over unemployment benefits, cuts in Medicare payments to doctors, taxes on large inheritances, and how to limit the impact of the alternative minimum tax, a parallel income tax system that is intended to ensure the rich pay a fair share but that is increasingly encroaching on the middle class.
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President Obama said that if talks between the Senate leaders break down, he wanted the Senate to call an up-or-down vote on a narrower measure that would extend only the middle-class tax breaks and unemployment benefits.
If Congress is unable to act before the new year, Washington will have effectively ushered in a series of automatic tax increases and a program of drastic spending cuts that economists say could pitch the country back into recession.
The president and lawmakers put those spending cuts and tax increases in place this year as draconian incentives that would force them to confront the nation’s growing debt. Now, lawmakers are doing everything they can to keep them from happening.
‘‘We just can’t afford a politically self-inflicted wound to our economy,’’ Obama said Saturday in his weekly address. ‘‘The housing market is healing, but that could stall if folks are seeing smaller paychecks. The unemployment rate is the lowest it’s been since 2008, but already, families and businesses are starting to hold back because of the dysfunction they see in Washington.’’
The fear of another painful economic slowdown appears to have accelerated deal making on Capitol Hill with just 48 hours left before the so-called fiscal cliff arrives.
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Weeks of public sniping between Senators Harry Reid of Nevada, the Democratic leader, and Mitch McConnell of Kentucky, the Republican leader, ebbed on Friday evening with pledges of cooperation and optimism from both.
On Saturday, though, that sentiment was put to the test as 98 senators waited for word whether their leaders had come up with a proposal that might pass muster with members of both parties. The first votes in the Senate, if needed, are scheduled for Sunday afternoon.
‘‘It’s a little like playing Russian roulette with the economy,’’ said Senator Mark Warner, Democrat of Virginia. ‘‘The consequences could be enormous.’’
Members of Congress were mostly absent from the Capitol on Saturday, after two days of Senate votes on other matters and a day before both chambers were to reconvene. House members were scheduled to return from their districts. However, senior aides were working on proposals in their offices or at their homes.
Speaker John Boehner stopped by the Capitol briefly to see his chief of staff on Saturday afternoon. McConnell also paid a visit.
Aides to Reid were expecting to receive offers from McConnell’s staff, but no progress was reported by midday. Even if the talks were to take a positive turn, Senate aides said, no announcement was expected before the leaders briefed their caucuses on Sunday.
The chief sticking point among lawmakers and the president continued to be how to set tax rates for the next decade and beyond. Obama and Democrats have said they want tax rates to rise on income over $250,000 a year, while Republicans want a higher threshold, perhaps at $400,000.
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Immediately — regardless of whether Congress and Obama reach a deal — every working American’s taxes will go up because neither party is fighting to extend a Social Security payroll tax cut that has been in place for two years.
But failure to reach a broader deal on taxes and spending would increase taxes even further, returning rates to Clinton-era levels. Paychecks would shrink as employers start withholding more for taxes.
Many families would also suffer if Congress fails to extend emergency jobless benefits, meaning that 2.1 million Americans would abruptly stop receiving expected payments.
‘‘There’s going to be a hit to people who don’t have much capacity to absorb a hit,’’ said Christine L. Owens of the National Employment Law Project.