Negotiations are almost complete on a long-overdue farm bill that will set new spending levels for the federal food stamp program and add yet another wrinkle to the national debate over income inequality as Congress mulls how to help unemployed and low-wage workers.

Leaders of the House and Senate agriculture committees had planned to announce a deal on a new multiyear farm bill this week, but aides familiar with the talks said any such announcement might be pushed into next week because of differences about price controls on the nation’s dairy industry.

The delay comes as the Senate is debating a bipartisan proposal to extend unemployment benefits and congressional Democrats prepare for a push to increase the federal minimum wage.

Whenever the agreement is reached, it will be “one of the bipartisan highlights” of the congressional year, Senate Agriculture Committee Chairman Debbie Stabenow (D-Mich.) told reporters this week.

The farm bill affects roughly 16 million agricultural sector jobs nationwide, but most of the measure’s costs are tied to food stamps to help poor families.

View Graphic SNAP's average monthly benefits have risen steadily since the inception of the program.

Plans call for eliminating about $9 billion in funding for food stamps — formally known as the Supplemental Nutrition Assistance Program (SNAP) — over the next decade, according to several aides familiar with the negotiations who are not authorized to speak publicly about the details.

The cuts are a compromise between a proposed $4 billion reduction approved by the Democratic-led Senate in June and nearly $40 billion in cuts approved by the GOP-controlled House as Republicans sought to overhaul eligibility requirements for SNAP.

Aides said House and Senate lawmakers sought cuts to SNAP by focusing on what they call the “heat-and-eat” loophole.

In more than a dozen states and the District, the level of assistance provided to some SNAP beneficiaries is tied to eligibility for the federal Low Income Home Energy Assistance Program (LIHEAP). Such payments are usually made to apartment dwellers whose utility costs are included in monthly rent payments. In order to keep such low-income residents from choosing in winter months between paying a heating bill or buying groceries, the states provide minimal LIHEAP payments, often as low as $1, making them eligible for higher SNAP payments.

The negotiated farm bill would tweak the program by requiring states to pay at least $20 in heating assistance to eligible households. The change would reduce, but not eliminate, SNAP payments based on heat-and-eat eligibility and save nearly $9 billion, aides said.

The changes would affect at least 800,000 households, according to estimates by the Congressional Budget Office — a number small enough, aides said, that both liberal Democrats and conservative Republicans might support the compromise.

“I don’t think we should be focused on the cuts; I think we should be focused on the efficiencies of the program and who it’s genuinely helping,” said Rep. Marlin A. Stutzman (R-Ind.), a fiscal conservative who pushed for bolder changes to SNAP. Stutzman said he hasn’t decided how he will vote on the final bill.

Rep. Steve Southerland II (R-Fla.), another outspoken advocate for bolder reforms, said he also would reserve judgment: “I think that individual members are going to have to make their decision: Is my support of a farm bill based on a number or is it based on a meshing of the number and the policy reforms?”

Among congressional Democrats, some of the most liberal lawmakers expressed tentative support for the compromise.

Sen. Tom Harkin (D-Iowa), a longtime champion for the poor from one of the nation’s most prosperous farm states, said in a statement that “compared to the draconian cuts” sought by House Republicans, the negotiated change is “a dramatic improvement, particularly because it wouldn’t cut anyone from the program.”

Other liberal senators, including Jack Reed (D-R.I.) and Kirsten Gillibrand (D-N.Y.), signaled Wednesday that a higher level of cuts would force them to vote against the entire bill. Reed said he “would be very upset” if the cuts are included, while Gillibrand described the plan as “the wrong approach.”

Needy families receiving food aid “didn’t spend our nation into debt and we shouldn’t tighten the federal belt around their waists,” she said in a statement. In New York, Gillibrand said, nearly 300,000 families would lose about $90 in monthly assistance. “That’s the last week of groceries for the month,” she said.

Democratic aides said that lawmakers from Northeastern and Western states with large urban areas might also vote against the final bill.

Aides familiar with the negotiations said the most significant unresolved issue is whether to end price controls on the dairy industry, which Republicans argue have cost taxpayers billions of dollars and needlessly drive up the cost of milk, cheese and yogurt.

The issue is of special concern to House Speaker John A. Boehner (R-Ohio), who outlined his opposition to the price controls in a rare “Dear Colleague” letter to House lawmakers over the summer.

“The federal government doesn’t control the supply or price of bread, clothes, or cell phones — it shouldn’t be doing so for milk,” Boehner said in his letter.

Stabenow and House Agriculture Committee Chairman Frank D. Lucas (R-Okla.) led closed-door talks on the issue Wednesday, and Lucas described the topic as “a real challenge.”

“Like any complicated piece of legislation, there are lots of nuances and lots of opportunities for modification and improvement,” he told reporters.