WASHINGTON — Hovering in the background of the “fiscal cliff” debate is the prospect of 2 million people losing their unemployment benefits four days after Christmas.

“This is the real cliff,” said Sen. Jack Reed, D-R.I. He’s been leading the effort to include another extension of benefits for the long-term unemployed in any deal to avert looming tax increases and massive spending cuts in January.

“Many of these people are struggling to pay mortgages, to provide education for their children,” Reed said this past week as President Barack Obama and House Speaker John Boehner, R-Ohio, rejected each other’s opening offers for a deficit deal.

Emergency jobless benefits for about 2.1 million people out of work more than six months will cease Dec. 29, and 1 million more will lose them over the next three months if Congress doesn’t extend the assistance again.

Since the collapse of the economy in 2008, the government has poured $520 billion — an amount equal to about half its annual deficit in recent years — into unemployment benefit extensions.

White House officials have assured Democrats that Obama is committed to extending them another year, at a cost of about $30 billion, as part of an agreement for sidestepping the fiscal cliff and reducing the size of annual increases in the federal debt.

“The White House has made it clear that it wants an extension,” said Michigan Rep. Sander Levin, the top Democrat on the House Ways and Means Committee.

Republicans have been relatively quiet on the issue lately. They demanded and won savings elsewhere to offset the cost of this year’s extension, requiring the government to sell some of its broadcasting airwaves and making newly hired federal workers contribute more toward their pensions.

Boehner did not include jobless benefits in his counteroffer response this past week to Obama’s call for $1.6 trillion in new taxes over the next decade, including raising the top marginal rates for the highest-paid 2 percent.

Long-term unemployment remains a persistent problem. About 5 million people have been out of work for six months or more, according to the Bureau of labor Statistics. That’s about 40 percent of all unemployed workers.

The Labor Department said Friday that the unemployment rate fell to 7.7 percent from 7.9 percent, the lowest in nearly four years. But much of the decline was due to people so discouraged about finding a job that they quit looking for one.

Democrats have tried to keep a flame burning under the issue. Ending the extended benefits would “deal a devastating blow to our economy,” 42 Democratic senators wrote Senate Majority Leader Harry Reid, D-Nev., this past week.

The Congressional Budget Office said in a study last month that extending the current level of long-term unemployment benefits another year would add 300,000 jobs to the economy. The average benefit of about $300 a week tends to get spent quickly for food, rent and other basic necessities, the report said, stimulating the economy.

The liberal-leaning Economic Policy Institute found that extended unemployment benefits lifted 2.3 million Americans out of poverty last year, including 600,000 children.

States provide the first 20 weeks to 26 weeks of unemployment benefits for eligible workers who are seeking jobs. When those are exhausted, federal benefits kick in for up to 47 more weeks, depending on the state’s unemployment rate.

The higher a state’s unemployment rate, the longer state residents can qualify for additional weeks of federal unemployment benefits. Only seven states with jobless rates of 9 percent or more now qualify for all 47 weeks.

Congress already cut back federal jobless benefits this year. Taken together with what states offer, the benefits could last up to 99 weeks. Cutting the maximum to 73 weeks has already cut off benefits to about 500,000 people.

Opponents of benefit extensions argue that they can be a disincentive for taking a job.

“Prolonged benefits lead some unemployed workers to spend too much time looking for jobs that they would prefer to find, rather than focusing on jobs that they are more likely to find,” said James Sherk, a labor policy analyst at the conservative Heritage Foundation.

But Sen. Tom Harkin, D-Iowa, noted that unemployment checks add up to about $15,000 a year. “That’s poverty level,” he said. “This is not something people just want to continue on; they want to get jobs.”