WASHINGTON — A plan by House leaders to cut $40 billion from the food stamp program — twice the amount of cuts proposed in a House bill that failed in June — threatens to derail efforts by the House and Senate to work together to complete a farm bill before agriculture programs expire on Sept. 30.

The bill that would double cuts previously sought by House Republicans was announced Thursday by Representative Frank D. Lucas, Republican of Oklahoma and chairman of House Agriculture Committee, during a lunch with lobbyists, and first reported by Reuters.

Representative Eric Cantor Republican of Virginia, the House majority leader, said a vote on the deeper food stamp cuts would take place before meeting with senators to iron out the differences between the House and Senate farm bills.

The Senate passed its version in May. The House approved its bill last month but did not include the food stamps program, after a vote on a comprehensive farm bill failed in June.