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The president’s annual budget is due in February, though it is unlikely that it will gain much — if any — traction, as both houses of Congress overwhelmingly rejected the president’s proposal last year.

Also looming is the federal government’s self-imposed borrowing limit, which is expected to be reached by late February.

Republicans generally want a dollar of spending cuts for every dollar that the so-called debt ceiling is raised. Democrats accuse Republicans of holding the economy hostage because the financial markets likely would nose-dive if the government exceeds its borrowing limit and defaults on its loans. Mr. Obama has vowed not to bargain with lawmakers over a debt ceiling increase — as he did in the summer 2011 standoff — but will be hard-pressed to impose his will on Republicans.

The new Congress also will be pressed to deal with renewing the payroll-tax “holiday” that expired for more than 160 million American workers at the end of 2012.

The 2 percentage point Social Security tax cut allowed a worker earning $50,000 to keep about an extra $19 a week. Mr. Obama pushed for the tax cut in 2010 as a way to increase workers’ take-home pay to help boost consumer spending and provide a spark for the economy. The initial tax cut was for only a year but was extended through 2012.

Despite Republicans’ appetite for tax cuts, many in the party question whether the payroll cut did much to stimulate the economy. They also said they were concerned that it threatened the independent revenue stream that funds Social Security.