Congress is on the verge of dramatically overhauling federal farm and nutrition policies affecting a broad range of issues, from how food is packaged and sold to how the government helps poor people pay for their groceries.

After three years of arduous haggling, the Senate is expected to give final passage Tuesday to a new five-year farm bill that the House passed last week. President Obama is expected to sign it when it gets to his desk. The $956.4 billion package has sailed through Congress in recent days with little opposition, making it a rare bipartisan accomplishment in an otherwise rancorous and unproductive era.

The legislation will eliminate billions of dollars in direct subsidy payments to the nation’s farmers. In their place, the bill creates a new crop insurance program. It also saves billions by consolidating government conservation programs and cuts about $8 billion in funding for food stamps by tweaking eligibility rules. The bill is supposed to cut roughly $16 billion in government spending over the next decade, according to government estimates — a modest sum but one in which proponents take considerable pride.

“We are the only part of the federal government to produce savings in our own areas of jurisdiction, and we eliminated about a hundred different programs or authorizations that . . . no longer made sense,” Debbie Stabenow (D-Mich.), chairman of the Senate’s agriculture committee, said Sunday in a C-SPAN interview that included questions from a Washington Post reporter. “And so I would challenge my colleagues — if they did what we did, we’d have a balanced budget.”

House Agriculture Committee Chairman Frank D. Lucas (R-Okla.) said negotiators always focused on ensuring that “a majority of the middle” would unite to pass the bill.

“I’m quite certain that my very conservative friends and my very liberal friends won’t be happy with the final product,” he said in a recent interview. “Whether you want to define that as good legislating or a sign of the times, the folks with the hard perspective on both sides will not be pleased.”

Since the bill’s formal release last week, lawmakers’ complaints about the proposed spending cuts have mostly come from the far left and far right.

On Monday, conservatives such as Sens. Tom Coburn (R-Okla.), Charles E. Grassley (R-

Iowa) and Jeff Sessions (R-Ala.) criticized negotiators for not cutting more, while Rep. Rosa L. DeLauro (D-Conn.), who voted against the bill last week, said food stamp cuts mean that “children will go to bed hungry and spend the next day at school unable to concentrate.”

The bill includes changes to complicated programs involving environmental regulations on farms, aid to dairy and sheep farmers, and what kind of food the Agriculture Department should buy to replenish the nation’s food banks.

But most of the political attention has focused on food stamps, formally known as the Supplemental Nutrition Assistance Program, or SNAP.

The program was a big concern of tea-party-leaning lawmakers who helped the GOP take control of the House in 2011. Negotiations over a new bill nearly collapsed in July when House GOP leaders, bending to the demands of tea party members, split apart the farm bill and held separate votes on measures setting most agricultural policy and another that would have slashed $40 billion in SNAP money by dramatically rewriting eligibility rules.

House and Senate negotiators ultimately agreed to cut about $8 billion by closing a loophole that several states and the District of Columbia have used to boost SNAP payments to low-income households.

That change will reduce benefits for about 850,000 households nationwide, according to estimates by the Congressional Budget Office.

In a nod to conservative concerns about the size of SNAP expenditures, the measure slashes the USDA’s advertising budget for the program, and the department will need to ensure that illegal immigrants, lottery winners, college students and the dead cannot receive food stamps and that beneficiaries cannot collect payments in multiple states.

But the legislation also creates a new program that will ­allow the poor to double their food stamp benefits at farmers markets, a move that advocates say will help tens of thousands of SNAP users eat more-nutritious foods.

Left unsettled by the 959-page bill are growing concerns about “country-of-origin labeling,” or wording that describes for grocery shoppers where the animals and birds that become meat and poultry are born, raised and slaughtered. The 2002 farm bill was the first to require producers to add the labeling. But representatives of the nation’s $44 billion livestock industry complained that the rules were too onerous, and in 2008 changes were made that no longer forced farmers to separate livestock based on where animals were born. The new bill makes no changes in that policy.

But a World Trade Organization ruling in 2012 led to new USDA rules last year. Now, labels must clearly state where an animal was born, where it was raised and where it was slaughtered.

The changes mean that farmers have to segregate animals based on place of birth and that slaughterhouses are having to do the same, according to industry leaders. Deliveries of pigs and cattle have to be carefully synchronized with processing plants so Canadian-born animals, for example, are not delivered when the plant is scheduled to slaughter Mexican- or U.S.-born animals. Ultimately, the cost of the changes could be passed on to consumers, they said.

“There is a cost all along the supply chain,” said Dave Warner, spokesman for the National Pork Producers Council. “The packer will not pay as much to the hog farmer for Canadian pigs now, because they have to shut down the lines to process them. As a result, the farmer won’t pay as much for the Canadian-born pigs.”

In the closing days of talks, some in the livestock industry tried unsuccessfully to get language inserted in the bill that would allow new labels to say something like “Product of U.S.” if the animal was born in Canada or Mexico but slaughtered in the United States.

“Our membership said this was our top priority and that we had to get it fixed,” said Colin Woodall, vice president of government affairs for the National Cattlemen’s Beef Association.

But the last-minute push failed.

Stabenow said in the C-SPAN interview that negotiators never focused on changing the labeling rules. “There was not support by a majority of Democrats or Republicans to eliminate the labeling for meat,” she said.

Lucas told reporters last week that “I thought there were enough good things in this farm bill . . . that we had to move forward.”

The issue could come to a head this month when the WTO holds a hearing on the labeling rules. A decision against the current rules could affect other industries if Mexico or Canada responds by imposing tariffs on American meat and poultry or other goods imported into their countries.