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Already entrenched over the issue, the chamber on Wednesday defeated an amendment from Rep. James P. McGovern, Massachusetts Democrat, by a 234-188 vote, that would have restored the $20 billion in SNAP reductions over the next 10 years by cutting subsidies to farmers.

The Senate cut food stamps less aggressively, shaving off about $400 million a year, or half a percent.

The bill was defeated hours after the House plowed through a slew of amendments, including one that replaced what Mr. Boehner called a “Soviet-style” dairy program with an insurance program that is commonly tied to other farm commodities.

After the bill’s defeat, Mr. Peterson called out to Mr. Lucas while reporters swarmed the men in the Speaker’s Lobby. But the agriculture chairman said he had to “go heal up.”

“I appreciate your work,” Mr. Lucas said.

“Yours too,” Mr. Peterson said. “We’ll figure it out.”