House Minority Leader Nancy Pelosi (D-Calif.) talks with Kentucky Gov. Steve Beshear (D) at the Capitol Visitors Center in Washington. (Chip Somodevilla/Getty Images)

With the holiday recess fast approaching, congressional negotiators were closing in on an agreement to avoid another government shutdown. But they faced a last-minute outcry from House Democrats demanding to extend federal jobless benefits as part of any deal.

“We are making a very clear statement that we cannot, cannot support a budget agreement that does not include unemployment insurance in the budget or as a sidebar in order to move it all along,” House Minority Leader Nancy Pelosi (Calif.) said Thursday after holding a hearing on the jobless program, which is set to lapse at the end of December, cutting off checks to 1.3 million people. “It would undermine who we are as a country.”

Later, Pelosi softened her remarks, saying Democratic support “depends on what the budget [deal] is” and is not contingent upon an agreement by reluctant Republicans to finance benefits for the long-term unemployed for a sixth year running.

But House GOP leaders are counting on Pelosi to deliver a large number of the votes they need to push a budget deal to final passage in the chamber. Democratic aides said her demands would give their chief negotiator, Senate Budget Committee Chairman Patty Murray (D-Wash.), leverage to extract concessions as the talks enter the last stage.

Murray and House Budget Committee Chairman Paul Ryan (R-Wis.) have been meeting for weeks to try to forge an agreement to replace sharp spending cuts known as the sequester and fund the government past Jan. 15, when the threat of a shutdown next looms.

The pair met briefly in Murray’s office off the Capitol Rotunda on Wednesday afternoon. And although they were headed home for the weekend, their aides planned to continue talking in hopes of sealing a deal early next week. That would let the House approve the plan and adjourn for the year on schedule next Friday.

Lawmakers and senior aides in both parties said they were optimistic about the prospects for a modest agreement that would restore about $45 billion to agency budgets in the current fiscal year and about $20 billion in fiscal 2015. To cover that cost — and to put another small dent in the federal deficit — negotiators are considering a range of policies, including cutting retirement benefits for federal workers, reducing payments to hospitals that treat the uninsured and increasing security fees for airline travelers.

Although it would fall far short of a long-sought “grand bargain” to raise taxes and rein in expensive health-care and retirement programs, such an agreement would at the very least give lawmakers — and the U.S. economy — a brief reprieve after three straight years of cascading fiscal crises.

“This is not an achievement, if it’s reached, to be minimized. We haven’t had a budget around here since 2009,” said Rep. Tom Cole (R-Okla.), a member of the conference committee tasked with forging a budget deal and a close ally of House Speaker John A. Boehner (R-Ohio).

Significant hurdles remain. Republicans are counting on an agreement that relies solely on alternative spending reductions to replace the sequester cuts, because conservatives oppose raising fees to increase spending. Fee increases, GOP aides said, can be part of the deal, but the proceeds must go entirely to deficit reduction.

But key Democrats, such as House Minority Whip Steny H. Hoyer (Md.), oppose one of the largest sources of new savings: asking federal employees to contribute more toward their own retirement. After facing several years of pay freezes and lost wages because of furloughs caused by the sequester, federal workers should not have to make additional sacrifices, he said.

“The only working people that have paid a price so far in trying to bring down the deficit are federal workers,” Hoyer said.

Recognizing the need to appease Democrats, Republicans have dialed back anticipated savings from civil-service pensions. Senior GOP aides said the final deal is likely to call for less than $17 billion in lower government contributions to employee retirement accounts — a smaller bite even than President Obama proposed in his most recent budget request.

But reducing the pool of savings means reducing the amount available for sequester relief. People in both parties worried that the final package could wind up being so small that many lawmakers would find it not worth the trouble.

“This has been a negotiation of subtraction,” said Rep. Chris Van Hollen (Md.), the chief budget negotiator for House Democrats. “When you start taking stuff off the table, you end up with a very narrow range of options.”

On Thursday, Van Hollen offered his vision for a much broader deal that not only would provide an additional $25 billion to extend emergency jobless benefits through 2014, but also would finance new spending on infrastructure and early childhood education. The expansive package calls for closing tax loopholes for corporations and counting savings from ending the wars in Iraq and Afghanistan to pay for the initiatives, policies Republicans strongly oppose.

At his weekly news conference Thursday, Boehner did not rule out the possibility of a deal to extend unemployment insurance. But, he said, Democrats have to find an acceptable way to pay for it.

“If the president has a plan for extending unemployment benefits,” Boehner said. “I would surely entertain taking a look at it.”