Reps. Marlin Stutzman of Indiana and Kristi Noem of South Dakota, two Republicans who helped design the bill, said the legislation would find the savings by tightening eligibility standards and imposing new work requirements. It would also likely try to reduce the rolls by requiring drug testing and barring convicted murderers, rapists and pedophiles from receiving food stamps.
Many provisions in the proposed bill were included in farm legislation defeated on the House floor in June, though several were added by amendment. The original farm bill passed by the House Agriculture Committee would have cut food stamps by about $2 billion a year, but conservatives revolted against the bill even after adding additional savings through amendments, saying the cuts weren't high enough.
After the farm bill defeat, Republican leaders split the legislation in two and passed a bill in July that included only farm programs. They promised a food stamp bill to come later, with deeper cuts.
A spokesman for Cantor said the proposed bill will "build on those reforms already considered by the House."
"That will include common-sense measures, such as work requirements and job training requirements for able-bodied adults without children receiving assistance, that enjoy a broad range of support," said Doug Heye.
Much of the estimated savings could come from requiring such adults to seek work, a provision that wasn't in the original bill. The law already requires that they eventually work or receive work training to receive SNAP, but the 2009 stimulus law and waivers issued by the Agriculture Department since then have allowed states to set aside those work requirements.
The proposed bill hasn't been released and its exact cost isn't yet known, but the Republicans are estimating the cuts would be around $4 billion annually.
A farm bill passed by the Senate in June keeps the food and farm programs together and cuts food stamps by about $400 million a year, or about half a percent. Senate Agriculture Chairwoman Debbie Stabenow, D-Mich., on Thursday accused House leaders of trying to block the farm bill by proposing something that the Senate would never accept.
"It's wasted time and effort, it's not going anywhere," she said. "It's not going to become law."
Current farm law expires at the end of September, and it's unlikely that both sides will agree on a final farm bill before then, even if the House is able to pass a food stamp bill. Food stamp dollars will continue to flow after the law expires but some farm programs would be in danger. Without an extension or a change in policy, for example, dairy subsidies would revert to decades-old law and cause milk prices to potentially double.
Senate Majority Leader Harry Reid has said he won't allow another extension after the law was continued once early this year to avert the dairy crisis. Stabenow said an extension would be difficult anyway because many members don't want to continue certain farm subsidies that would be eliminated under the House and Senate farm bills.
"This is a ticking time bomb here, waiting to go off," she said. "It makes no sense."
Minnesota Rep. Collin Peterson, the top Democrat on the House Agriculture Committee, said the proposed food stamp bill "effectively kills any hopes of passing a five-year farm bill this year."
House Agriculture Committee Chairman Frank Lucas, R-Okla., hinted Thursday that the differences are so "huge and dramatic" between the Senate bill and what the House is proposing, that the White House may need to get involved, something the Obama administration has so far declined to do. The White House supported the Senate bill but had threatened a veto of the House bill.
"This may be one of those issues that may need some guidance from on high," Lucas said.
First, though, Republicans have to get the votes to pass the food stamp bill in the House. That could be difficult as Democrats are likely to be united in opposition and some moderate Republicans may not go along.
Stutzman said he thinks the issue will play well with their constituents when members return to their districts in August. The Republicans say they are trying to focus on the policies, not the number of dollars that would be cut.
"Most people will agree that if you are an able bodied adult without any kids you should find your way off food stamps," Stutzman said, referring to the proposed work requirements. "I don't think we will find much disagreement on this."
Noem agreed, saying that talking about policies and not just dollars "shows that you really care about adding integrity into the program."
Still, she said, making cuts to the program is a "huge culture change" not only for Democrats but also for some Republicans who have a lot of food stamp recipients in their districts.
"That's all a big pill to swallow for some of them," she said.