WASHINGTON – A critical compromise to head off a year-end tax increase for millions of Americans took shape Thursday in private talks between the White House and congressional Republicans, and an extension of jobless benefits appeared likely to become part of any deal.

Democrats sought to expand the package with other provisions that officials said would accelerate the sluggish economic recovery. They included a tax break providing as much as $400 for individual working people and $800 for couples, even if they pay nothing to the IRS.

Two days after he and newly empowered Republicans exchanged pledges of cooperation at the White House, President Obama expressed optimism about the prospects for agreement in time for enactment by year’s end. Still, he cautioned, “That doesn’t mean there might not be some posturing over the next several days.”

Not long after Obama spoke, Democrats ignited a partisan row in the House with legislation that would prevent taxes from rising on lower- and middle-income wage earners but allow them to go up for people at higher incomes.

Given Republican objections, that measure has no chance of passing the Senate. But Democrats there insisted on voting on it today as a way to dramatize their support for the measure.

The president has already signaled he will accede to Republican demands for extending tax cuts at all income levels, making votes on the Democratic-backed bill purely symbolic.

The House measure drew criticism from Rep. John Boehner of Ohio, who will become the speaker when Republicans take power in January. “I am trying to catch my breath so I don’t refer to this as, uh, chicken crap, all right?” Boehner said.

“But this is nonsense, all right? The election was a month ago,” he said, referring to voting that swept Democrats from power in the House and reduced their majority in the Senate.

The bill passed, 234-188, largely along party lines. That was followed by a meeting in which Treasury Secretary Tim Geithner, Budget Director Jacob Lew and senior lawmakers discussed the compromise plan to extend existing cuts for taxpayers at all income levels.

The outlines of the measure include an extension of income tax cuts enacted while George W. Bush was president for an as-yet-undetermined period of time, perhaps two or three years. The bill is expected to apply to personal income-tax rates as well as capital gains, dividends, the alternative minimum tax, the so-called marriage penalty and more.

Any agreement on legislation extending tax cuts to those at upper income levels would mark a surrender on the part of the president, who has long argued the provision isn’t warranted in view of the $700 billion cost to the deficit if they last for 10 years.

At the same time, any measure that was limited to an extension of two or three years would leave Republicans with less than the permanent tax cuts they have long sought.

The impetus for an extension of expiring jobless benefits for the long-term unemployed came from the Democrats, although Republicans have signaled they are willing to agree as long as the cost doesn’t add to federal deficits.

Without action by Congress, unemployment benefits will run out this month for 2 million people, and several million more will lose them later in the winter. The benefits average $310 a week and go to unemployed workers who have been without jobs for 26 weeks or longer. The checks cut off after 99 weeks.