The D.C. Council is poised to pay more than 20,000 city employees, including council members, a combined $22 million this year to make up for the four unpaid holidays they were forced to take last year to quell budget pressures.

In his monthly news briefing Monday, council Chairman Kwame R. Brown said he and Mayor Vincent C. Gray agreed that a big chunk of an unexpected budget surplus for fiscal 2012 should go to pay the employees.

The council is scheduled to vote on the matter Tuesday. But the plan, a major victory for politically influential public-employee unions, is fueling a debate over whether the District’s surplus dollars should go to its 29,000-strong workforce when the city is considering tax increases and cuts to social-services programs.

“Clearly, we would love to give money back to everybody. . . . Unfortunately, you can’t,” said Brown (D). “The people who work every day in this city, that have been working hard and took their furlough days, deserve to get their money back, and that is what is on the table now.”

But Gray and Brown are pushing to spend a large share of the surplus in the fiscal 2012 budget on paying city employees for last year’s unpaid days.

At the time, Chief Financial Officer Natwar M. Gandhi projected a $188 million budget shortfall, prompting the furloughs on Presidents’ Day, Emancipation Day, Memorial Day and Independence Day. But in late January, Gray and Gandhi announced that the city had a surplus, leading critics to question some of the 2011 cuts and cost-saving actions.

In 2010, organized labor and city employees played a crucial role in Gray’s successful campaign to unseat Mayor Adrian M. Fenty (D). Public-employee unions have also been crucial backers of several council members.

“Four days may not seem like a lot of days to a lot of people, but if I lose a day, it might kill me,” said George Johnson, executive director of the local chapter of the American Federation of State, County and Municipal Employees.

Brown denies that politics influenced the decision to pay the employees, noting that money will go to unionized and management city workers.

“This is not employee unions getting their money back,” Brown said. “Everyone [in District government] is getting their money back.”

Because council members also had to give up four paid holidays last year, they also will be eligible if the plan is approved Tuesday.

Brown said he will not accept the money.