WASHINGTON — Approval of a massive farm bill — and the cost of a gallon of milk — could hinge on a proposed new dairy program the House is expected to vote on this week.

An overhaul of dairy policy and a new insurance program for dairy farmers included in the farm bill have passionately divided farm-state lawmakers. Most importantly, it has caused a rift between House Speaker John Boehner, R-Ohio, and the top Democrat on the House Agriculture Committee, Rep. Collin Peterson of Minnesota.

The bill sets policy for farm and nutrition programs, including food stamps. And House Agriculture Chairman Frank Lucas, R-Okla., will need Boehner and Peterson to bring in votes from the moderate wing of each party if the bill is to pass. Many conservative Republicans and liberal Democrats, especially those from districts with little agriculture, are expected to vote against it due to concerns over cuts to food stamps.

The proposed dairy program would do away with current price supports and allow farmers to purchase a new kind of insurance that pays out when the gap between the price they receive for milk and their feed costs narrows. The program is voluntary, but farmers who participate also would have to sign up for a so-called market stabilization program that could dictate production cuts when oversupply drives down prices.

The idea is to break the cycle in which milk prices drop and farmers produce more to pay their bills, flooding the market and forcing prices down further.

Peterson wrote the proposed dairy policy, which Boehner last year compared to communism. Boehner is backing an amendment by the chairman of the House Judiciary Committee, Virginia Republican Robert Goodlatte, which would scale it back.

“I’m caught between two raging bulls in a pasture,” Lucas joked as he lobbied colleagues.

Peterson said the stabilization program would prevent a recurrence of what happened in 2009, when many dairy producers went out of business after they were hit hard by a combination of low milk prices and high feed costs.