Congressional negotiators are said to be nearing a budget proposal for next year that would achieve the bare minimum -- setting basic spending levels to avoid a partial government shutdown, and tinkering around the edges of the sequester. 

Sources tell Fox News that House and Senate negotiators are close on a possible agreement, at least on paper. Lawmakers have until Friday to finish off their work for the year. 

"'Close' is a staff term," one senior lawmaker cautioned, suggesting it's unclear whether those drafting the bill yet have the votes. 

But even if the bill comes together by the time the House is set to adjourn for the year on Friday, it represents a far cry from the kind of "grand bargain" congressional leaders once talked about. 

The Washington Post reported that it would not include any significant tax or entitlement reforms, or seriously deal with the sequester cuts. The national debt would continue its seemingly inexorable climb. 

Aides told the Post that the emerging plan would raise agency spending to just over $1 trillion for the next two fiscal years, while aiming to offset some of that spending by cutting federal worker pensions and making other modest changes. 

Though lawmakers once considered a pension overhaul that would save $130 billion over a decade, aides reportedly are looking at a plan that will instead save less than $17 billion. 

The Post reports that negotiators are hoping to finish off the bill in a matter of days and take it straight to the floors of the House and Senate. Lawmakers have until Jan. 15 to pass a budget bill or else risk a partial shutdown. 

The budget, though, just represents one challenge facing Congress in the days ahead. While the current budget bill expires in mid-January, lawmakers have until only the end of the year to deal with several other items, including payments to doctors and long-term jobless benefits. 

On top of that, several lawmakers, and President Obama, were rearranging their schedules to attend memorial services this week for the late South African leader Nelson Mandela. 

Long-term unemployment aid, a prickly issue on the Hill, is expected to expire on Dec. 28 for 1.3 million workers who've been without a job for longer than six months. 

President Obama used his weekly radio address on Saturday to appeal to Congress to extend it. "Extending unemployment insurance isn't just the right thing to do for our families -- it's the smart thing to do for our economy," he said. 

But despite threats by some Democrats to hold up the must-pass budget bill over their demand for extending jobless benefits, a top Democrat signaled Sunday that his party might not block the budget bill over the issue. 

"I don't think we've reached that point where we've said this is it, take it or leave it," Illinois Sen. Dick Durbin, the No. 2 Democrat in the Senate, said on ABC's "This Week." 

Speaking on "Fox News Sunday," Sen. Rand Paul, R-Ky., said the long-term benefits -- which typically kick in after 26 weeks -- are actually doing a "disservice to these workers" by making them less marketable to would-be employers. 

Sen. Rob Portman, R-Ohio, speaking on the same program as Durbin, said the issue should be dealt with separately, outside the budget talks. 

Both Portman and Durbin, though, voiced optimism that lawmakers might reach some kind of agreement on the budget by the end of the week. 

Lawmakers are also at work drafting a three-month measure to prevent a 24 percent drop in Medicare payments to doctors. The cost is estimated at about $8 billion. 

And lawmakers are trying to work out at least a short-term deal over the farm bill -- an issue that could end up affecting the price of milk. 

The bill itself is meant to set spending levels for farm programs and food stamps. A House measure that passed on a party-line vote calls for food stamp cuts totaling $40 billion over a decade. A Senate version, passed with bipartisan support, envisions reductions of $4 billion. 

But failure to resolve the broader issues would also return the nation to a Depression-era dairy law and set in motion a chain of events that would potentially quadruple the price of a gallon of milk. 

Fox News' Chad Pergram and The Associated Press contributed to this report.