WASHINGTON — Prospects for passage of a new farm bill before the end of the year appear dim, with just a week left before Congress adjourns for the holidays, although lawmakers insisted they were close to a deal.

The current measure expires at the end of the month. Members of the House and Senate have been meeting to reconcile their different versions of a new bill, and they agree on many things, including expanding crop insurance for farmers. But they remain far apart on issues like cuts to the food stamp program. A House proposal would cut about $40 billion from the program, while a Senate version would trim roughly $4.5 billion, mainly by making administrative changes.

Despite the differences, Senator Debbie Stabenow, Democrat of Michigan and chairwoman of the Senate Agriculture Committee, and Representative Frank D. Lucas, Republican of Oklahoma, who heads the House Agriculture Committee, say they have made significant gains in trying to work out a deal that would pass both houses.

“Chairman Lucas and I are working in good faith to produce a conference report that’s good for farmers, ranchers and families,” Ms. Stabenow said.