WASHINGTON — Democratic and Republican congressional leaders expressed optimism Thursday at prospects for swift compromise to extend Social Security tax cuts, keep long-term jobless benefits flowing and avoid a partial government shutdown at midnight Friday.

A third year-end bill, was cleared for final passage.

“Right now, Congress needs to make sure that 160 million working Americans don’t see their taxes go up on Jan. 1,” said President Barack Obama, referring to the tax cut extension.

House Speaker John Boehner of Ohio agreed. “We can extend payroll tax relief for American workers, help create new jobs and keep the government running. And frankly, we can do it in a bipartisan way,” he said.

In the Capitol, the previous day’s bristling rhetoric and partisan jabs all but vanished.

Republicans agreed to consider changes to a $1 trillion spending bill compromise that they and at least one Democrat said had been wrapped up days ago. The White House said it wanted adjustments.

There were separate negotiations on legislation to extend the Social Security payroll tax cut and unemployment benefits. Democrats abandoned their demand for a surtax on million-dollar incomes that they wanted to include in the measure, removing a provision that Republicans opposed.