WASHINGTON — A New Year’s deadline that could send the price of milk skyward looms over congressional negotiators as they try to reach agreement on a five-year farm bill. They’ve been tripped up by differences over the nation’s food stamp program and how to restructure farm subsidies.

The House and Senate agriculture committees have been far apart on both issues for more than two years. But after a private meeting Wednesday, the committee leaders expressed optimism that they may be able to find resolution in time to narrowly avert the expiration of dairy subsidies on Jan. 1. If those subsidies expire, new laws will kick in that could result in decreased dairy supply on the commercial market and higher prices for a gallon of milk.

Rep. Mike Conaway of Texas, a Republican on the House-Senate farm bill conference committee, said negotiators could possibly hold a public meeting next week for the conference committee to settle some of the remaining issues before the House leaves for the year on Dec. 13. But with a final deal still elusive, it seems unlikely that Congress will finish the bill before the end of the year.

On Thursday, House Speaker John Boehner said the bill should be extended through January while negotiators work out their differences. Boehner also contradicted the optimism of House Agriculture Committee Chairman Frank Lucas, R-Okla., who said Wednesday that the two sides had made “great progress.”

Finding a compromise on cuts to the nation’s $80 billion-a-year food stamp program has been the toughest obstacle over the past two years. The House passed a bill this summer that would cut $4 billion annually from food stamps – now known as the Supplemental Nutrition Assistance Program, or SNAP – and allow states to create new work requirements for some recipients. The Democratic Senate, backed by President Obama, passed a farm bill with a $400 million annual cut, one-tenth of the House cut.

Negotiators are also working out how farm subsidies should be restructured in the absence of a traditional subsidy called direct payments, which are paid to farmers regardless of crop price or crop yield. Both chambers’ bills would eliminate this $5 billion annual subsidy in response to critics who say it pays farmers not to farm. But they have argued over how to replace those payments, with major farm groups squabbling over whether subsidies should kick in based on crop prices or farmer revenue, and how to count the acreage on which the subsidies are based.

Minnesota Rep. Collin Peterson, the top Democrat on the House Agriculture Committee, said negotiators had tentatively resolved some of those subsidy issues. But they are still waiting for analysis of how much their proposals would cost, a process that could take until next week.

If the negotiators can’t agree on a bill and Congress allows the dairy supports to expire, a 1930s- and 1940s-era “permanent” farm law would go into effect. Those laws would raise the price that the government currently pays to purchase dairy products, prompting many processors to sell to the government instead of commercial markets. That would decrease commercial supply and consequently raise prices for shoppers at grocery stores.

Prices wouldn’t go up immediately, because the Agriculture Department would have to write the new rules based on the old laws and then put them in place. But Agriculture Secretary Tom Vilsack is warning that it may not take that long, saying the USDA was prepared to implement the dairy law in “short order” if the current law expires.

“That’s not something that I want to do,” Vilsack said. “I’m reasonably certain that’s not anything that anybody in Congress would want to have happen, and I’m sure that no consumer is anxious to see that happen. So hopefully we continue to see progress.”