WASHINGTON — As President Obama and Republican leaders try to avoid automatic spending cuts and tax increases beginning in the new year, several lawmakers say a stalled farm bill that reshapes nutrition and agriculture programs could contribute billions of dollars in savings.

Senator Debbie Stabenow, Democrat of Michigan and chairwoman of the Senate Agriculture Committee, and Representative Frank D. Lucas, Republican of Oklahoma and chairman of the House Agriculture Committee, are trying to persuade administration and Congressional leaders to include the measure in negotiations that are seeking to avoid more than $500 billion in tax increases and more than $100 billion in automatic spending cuts that would go into effect next year.

Both lawmakers have sponsored versions of a farm bill with steep spending cuts that would help with deficit reduction, they said.

“The Farm Bill is the only bipartisan deficit reduction bill that passed the Senate this year. It’s only natural it should be part of a larger deficit reduction agreement,” said Ms. Stabenow, who along with other leaders of the House and Senate agriculture committees, met last week with Agriculture Secretary Tom Vilsack to discuss including a new five-year bill in any deal between the White House and Congress.