Put this in the “small accomplishments” category for an especially gridlocked Congress: It appears increasingly likely that, with little fuss, lawmakers will approve a bipartisan compromise in coming days that will keep government running past Friday, when a short-term funding measure that has kept the lights on expires.

Partisan clashes have brought the government to the brink of a shutdown three times in the past year. But this time, appropriators from the House and Senate have been quietly working toward the unveiling, expected late Monday, of a compromise spending measure that would outline how government agencies should spend nearly $1 trillion through Sept. 30, 2012.

One thing the negotiators have had going for them is that they’ve been given space to work, their efforts largely overshadowed by a bitter fight between Republicans and President Obama over extending a one-year cut in the payroll tax, paid by 160 million workers, when it lapses at the end of the month.

It’s also helped that Congress agreed to an overall spending level for the year — often the most contentious issue — as part of the August debt deal. And talks have been smoothed as both parties have come to grips with the need for compromise. While Republicans hold a majority in the House, it has become clear that a bloc of several dozen members who want dramatic spending cuts will probably oppose almost any appropriations deal, meaning that Republicans need Democratic votes to get a bill passed.

The payroll tax fight will continue this week as the House votes on a GOP-authored proposal that would link the extension of the tax cut sought by Obama with Republican priorities, including a measure to speed the construction of the controversial Keystone XL oil pipeline.

On Sunday, Senate Minority Leader Mitch McConnell (R-Ky.) predicted that some Democrats who support construction of the 1,700-mile pipeline from Canada to the Gulf Coast would vote for the Republican bill.

But Senate Majority Leader Harry M. Reid (D-Nev.) has said the GOP measure is a “partisan joke” that cannot win approval in the Democratic-controlled Senate. Speaking Sunday on NBC’s “Meet the Press,” Sen. Lindsey O. Graham (R-S.C.) acknowledged that the pipeline was “probably not going to sell.” He predicted that Congress would find a way to broker a different bipartisan compromise to extend the tax cut.

Before concluding work for the year, Congress must tackle other major issues as well, including figuring out how to avert a scheduled deep cut in reimbursement rates paid to doctors under Medicare and whether to extend benefits for the unemployed.

Lawmakers had hoped to settle all of the issues and leave town by the end of this week. But members are already preparing for the possibility that continued disputes could force them to remain in session over the weekend and beyond.

Even so, leaders in both parties have been increasingly optimistic that one task that won’t hold things up is Congress’s most basic job: funding the government. They hope to bring the spending compromise to a vote this week and spare Washington the specter of another shutdown drama for nearly a year.

House Appropriations Committee Chairman Harold Rogers (R-Ky.) said late last week that it was his “hope and expectation” that the process would conclude this week.

His Senate counterpart, Daniel K. Inouye (D-Hawaii), said he was “confident” that talks were “on a path” to conclude before the holiday recess.

The negotiations have been eased by the August debt deal, in which Congress agreed to cap discretionary spending at $1.043 trillion for fiscal 2012, a figure that represents a 1.5 percent cut from the year that ended Sept. 30.

With the overall spending level for the year set, members of the appropriations committees have been able to turn to the detailed work of deciding how to divvy up spending among various federal programs.

The dynamics of the talks have also been shaped by the awareness by all involved that a bloc of several dozen House Republicans is likely to oppose whatever bill emerges.

That pattern has been established in spending votes this year, including in September, when 53 House Republicans voted against a short-term funding bill that kept government running through late last month.

Again last month, 101 House Republicans voted no on a measure that settled funding for five federal departments — Agriculture, Commerce, Housing and Urban Development, Justice, and Transportation — through next September.

Approved with a bipartisan majority, that measure also provided temporary funding for the rest of government, that lasts through Friday.

The bill under consideration this week is intended to set funding priorities for the other three-fourths of the government, including the Defense Department and war spending, for the remainder of the fiscal year.

The repeated defections of rank-and-file Republicans mean that GOP leaders know they must broker a compromise with House Democrats to get a spending bill through their own chamber, much less the Senate.

The contentious payroll-tax debate has also served to provide cover for the appropriations discussions to continue with little attention.

Despite the progress, members of the House and Senate appropriations committees spent the weekend tangling over a series of policy proposals that could still threaten the measure’s easy passage.

Those discussions have been especially tricky over the part of the bill funding the departments of Labor, Health and Human Services, and Education and another part that would provide money for the Interior Department and other environmental agencies. These are areas loaded with high-profile policy implications, including abortion rights, the Obama health-care law and environmental regulations. But although congressional aides acknowledged that a last-minute snag could still crop up in a Congress prone to unexpected blowups, the aides say steady progress has been made toward a compromise.

Members of Congress conducting the hard work of spending negotiations said the public should take heart from the rare evidence of legislative compromise.

Rep. Norm Dicks (Wash.), the ranking Democrat on the House Appropriations Committee, called the group “the last bastion of getting something done around here.”

A compromise, Inouye added, would “show that reasonable people are able to reach reasonable agreements.”

Staff writer Felicia Sonmez contributed to this report.