U.S. leaders are edging closer to a compromise on contentious end-of-year mandates for sharp spending cuts in key government programs and tax increases for almost all American workers.

Significant hurdles remain to a deal, but the outlines of an agreement seemed to be emerging Tuesday, even as U.S. President Barack Obama and his Republican opponents in Congress spar over the details.

Throughout his successful re-election campaign, Mr. Obama called for ending a tax break for the wealthiest households, those making $250,000 a year. But now the president, a Democrat, says he is willing to keep the tax cut for those earning up to $400,000 annually. The leader of the Republican-controlled House of Representatives, Speaker John Boehner, wants the tax break extended for couples making up to $1 million.

Mr. Obama also reduced his demand for mores taxes over the next decade from $1.4 trillion to $1.2 trillion and said he would agree to a Republican call to curb spending for government pensions for retired workers by changing the way annual increases in the payments are calculated.

Even as they move closer to an agreement, the problem for both Mr. Obama and Boehner is whether they can convince their political colleagues to support the emerging compromise. In the U.S., Democrats have adamantly opposed any changes in Social Security, the pension plan for retirees, while Republicans have steadfastly stood against any tax increases, even for the wealthiest households.

The two sides are trying to avoid what Washington is calling a “fiscal cliff,” about $500 billion in mandated spending cuts for defense and domestic programs and higher taxes throughout the U.S. labor force that are set to take effect January 1.