Congress heads into a 24-day stretch Monday with a final chance to reach several bipartisan compromises that could steady the government’s shaky fiscal foundation and provide a slight boost to a sagging economy.

With both houses of Congress in session together for the first time in nearly three weeks, lawmakers must dig into the final details of the annual spending bills for 2012 and consider more of President Obama’s jobs legislation, while a dozen other lawmakers on a special deficit committee face a Nov. 23 deadline to craft a debt-reduction package.

Sen. Patty Murray (D-Wash.) exited a meeting of the “supercommittee” last week with a weary look. “I’m smiling,” she said, before acknowledging it was a forced smile. She then summed up the pressure that her panel and the entire Congress faces these next few weeks.

“There is no change in the weight that all of us feel,” said Murray, the Democratic co-chairman of the panel.

Republicans agree the tasks are daunting. “You’ve got all that to do, and then determine when we’re gonna leave, based upon: It’s all gotta be done by the 23rd,” House Majority Whip Kevin McCarthy (R-Calif.) said, noting the funding deadline is Nov. 18 and the committee’s deadline a few days later.

The first order of business will be assuring that the federal government does not endure another crisis over a potential shutdown, something that has already happened three times this year. Leaders are hoping Senate action early in the week on a measure outlining spending through September 2012 for some government agencies might pave the way to a broader deal on the year’s spending.

The Senate is expected to approve a $182 billion measure to fund agriculture, criminal justice, transportation and housing agencies through September. The bill groups together three of the 12 spending measures that Congress is supposed to consider separately and approve before the fiscal year ends Sept. 30.

House Appropriations Chairman Hal Rogers (R-Ky.) said last week that House and Senate appropriators have made progress. The goal, he said, will be to quickly come up with a compromise measure that would settle spending for those government functions through the 2012 fiscal year, then attach a resolution keeping the rest of government operating under the same spending policies as last year into December.

This would allow time for Congress to work out its differences in the remaining spending bills, including much more expensive areas such as the Pentagon and the Department of Health and Human Services.

“None of this is set in concrete. We’re finding our way as we go,” Rogers said. “There are land mines every inch of the way.”

The supercommittee returns to work Tuesday with a public hearing. They will hear testimony from leaders of past task forces that also examined deficit reduction; they are likely to advocate for a higher level of savings than now appears possible, given last week’s blow-up on the panel.

At a closed-door meeting last Tuesday, Democrats offered a package that would shave $3 trillion off future debt projections, in part by raising $1.3 trillion in new tax revenue. Republicans, steadfastly opposed to new taxes, rejected that and offered their own measure of more than $2 trillion in savings with steeper cuts to entitlement programs. Democrats rejected it out of hand, saying that their own offer at least contained some political pain for both sides.

The group left a closed-door huddle Thursday for a weekend spent in separate corners, with no more private talks scheduled until after the public hearing. That hearing may serve as a barometer for whether the evenly divided panel can hunker down these next three weeks to craft the minimum level of $1.2 trillion in savings.

The group was formed from the August legislation that lifted the federal debt ceiling. If the 12-member panel fails to approve a plan to meet its minimum savings goal, then automatic cuts will be imposed on federal agencies worth $1.2 trillion, half of which will come from national security budgets.

Meanwhile, the supercommittee’s work is the only likely vehicle for attaching some portions of Obama’s $447 billion jobs package — which has already been rejected, in total, by the Senate. Instead, Senate Democratic leaders have been bringing forward pieces of it, trying to win political leverage in the face of repeated Republican filibusters.

However, the House last week passed — by a wide bipartisan vote — legislation to end a program, set to begin in 2013, that would impose a withholding fee on government contracts. That and other pieces of the Obama proposal, particularly an expansion of the temporary payroll tax, are likely to be added to the supercommittee legislation.

Any package receiving majority support from the committee would be sent to the House and Senate floor for expedited consideration in December.

With Halloween on her mind, Murray joked that she might show up at Tuesday’s hearing in a costume to bond with her Republican co-chairman, Rep. Jeb Hensarling of Texas.

“I’m coming as Jeb,” she quipped.