Next week, Congress is expected to revive an old but increasingly rare tradition that may determine how well and how quickly the institution is able to recover from all the negative fallout of the recent government shutdown.

More than three dozen members of the House and Senate plan to sit down in a room together and begin sorting out big differences on competing versions of a large piece of legislation.

Members of the House and Senate agriculture committees announced plans Wednesday to begin meeting to negotiate details of a new Farm Bill. The agriculture conference committee is a back-to-the-future moment for Congress, which in recent years has subverted the once long-standing practice of having conferees from the House and Senate meet to negotiate final versions of legislation passed in each chamber.

That process has been largely replaced by deals struck between leaders that must then be ratified by each body, usually in the face of some crucial deadline. As part of the deal that ended the government shutdown, members of the House and Senate budget committees are also scheduled to begin talks about how to fund the government beyond Jan. 15. The outcome of that conference committee will determine the extent to which Republicans and Democrats can bridge the divide that led to the government shutdown.

Once considered among the most sacred “must-pass” measures, the Farm Bill affects about 16 million U.S. jobs and provides billions in food stamp aid.

“It’s far more than just a Farm Bill,” Agriculture Secretary Tom Vilsack said Wednesday. “It’s an energy bill. It’s a trade bill. It’s a jobs bill. It’s a conservation bill. It’s a food bill, and it’s a debt-and-deficit reduction bill. There are enormous benefits to all of America.”

For two years, lawmakers have blown through temporary deadlines to reauthorize the bill, but they now seem more eager to act.

“It’s long overdue,” said Sen. Debbie Stabenow (D-Mich.), who chairs the Agriculture Committee.

She has worked with members of both parties and chambers for more than two years to identify billions in savings that will be needed as part of a final budget agreement.

Rep. Frank D. Lucas (R-Okla.), the House Agriculture Committee chairman, will chair the meetings, which will begin Wednesday afternoon with a format that permits all 41 members to make public statements. From there, the path forward is unclear. The fine print of the House and Senate bills are similar, meaning most of the fighting will be over funding for food stamps, or the Supplemental Nutrition Assistance Program.

“I personally believe that we can come up with a consensus bill,” Lucas said Wednesday.

He added later: “If the committee can work it out, I want to work it out in committee. But if we can’t . . . then we may have to have some outside help.”

That help would come from House and Senate leaders, who voted for starkly different proposals. The Senate bill, passed in June with bipartisan support, would cut about $4 billion from food stamps over the next decade. The House’s Republican-backed measure would slash almost $40 billion in food stamp funding over the next decade, mostly by rewriting eligibility rules for beneficiaries.

Stabenow said Senate Democrats will oppose cuts much higher than those they’ve approved.

“I’m willing to look for other savings, based on tackling fraud and abuse, but I’m not going to just arbitrarily hurt people who may need for the first time in their lives temporary help because they lost their jobs,” she said.

Failure to pass a deal by Jan. 1 could mean a rolling series of changes that affect several commodities and grocery prices. Changes would begin almost immediately with the price of milk, which could rise to more than $3 per gallon because federal dairy policy would revert to a 1949 law.

The Agriculture Department is already taking steps to deal with temporary changes in dairy prices, and Vilsack said that congressional inaction would eventually stretch to the price and supply of other staples, including rice, wheat and corn.