The sparring mayoral candidates found one point to agree on with each other, municipal unions and even the WABC-TV reporter who posed the question at Tuesday’s debate: the next mayor and the unions should negotiate behind closed doors.

City employees have been working without union contracts since 2009 in some cases and the next mayor is going to have to devise a way to pay all 306,000 of them retroactive and future wage increases. Both the rising costs of union health plans and the expected break from the Bloomberg Administration will figure in the balance.

“Part of the political calculation is that the unions figure that if the mayor’s offering zeros, then the next mayor can’t offer anything worse,” said Maria Doulis, director of New York City studies at the Citizens Budget Commission.

Retroactive and future raises for city workers—who earn less than their private counterparts—will carry a steep tab. The Citizens Budget Commission estimates the raises will cost around $8 billion after inflation, while the Independent Budget Office predicts a $4.5 billion cost this year and $1.8 billion each year after using a model of the likely outcomes of negotiations.

There aren’t enough funds in budget reserves for back pay, but a new agreement without retro pay and future raises would run counter to “customary municipal labor relations in the city,” according to a March 2013 IBO report. The expired union contracts are one of the most serious challenges to the city’s fiscal health, the report notes.

The next mayor might need to scale back workers’ health plans to pay for some of the future raises. More than 90 percent of city workers have individual or family health plans with no employee contribution, a benefit enjoyed by less than 7 percent of private workers and few public sector employees, according to a January 2013 report by the Citizens Budget Commission.

With the $4.8 billion the city spent on employee health benefits in fiscal 2012 set to grow to almost $7 billion by fiscal 2016, the report recommends that the city require employees to pay some part of their health premiums and pare back its full reimbursements for Medicare Part B premiums.

Possible retroactive increases for teachers, police officers and other municipal employees are the sticking point in negotiations that haven’t yielded any agreements in the current round of bargaining between the city and the Municipal Labor Committee, a coalition of unions such as the United Federation of Teachers and District Council 37. Teachers and principals have yet to win the 4% wage increases other unions picked up in the prior bargaining term.

A spokesman for the Municipal Labor Committee declined to comment for this story. But Antoinette Isabel-Jones of the Council of School Supervisors and Administrators said in an email statement that the raises won’t bust the city’s budget.

“We understand that the subject of retroactive pay is a complicated one for the next mayor, but we firmly believe that our members are entitled to it, as they have been in years past,” she wrote.

Though De Blasio’s campaign declined to respond to requests for comment on the matter, the public advocate has indicated he’s open to retroactive increases. He just hasn’t said the extent of the raises or how he’ll pay for them. He pledged to negotiate “respectfully and privately” with city workers during Tuesday’s debate.

“If there’s going to be any discussion of retroactive, it will come because we find cost savings, from work rules or other areas,” said De Blasio. “But the bottom line is we have to balance our budget.”

Republican candidate Joe Lhota has rejected any back raises for city workers, but campaign spokeswoman Jessica Proud wrote in an email statement he would “negotiate a fair contract with the workers and the taxpayers that will include a raise going forward.”

Lhota and other opponents of retroactive increases maintain that the city doesn’t have the necessary funds in the budget for whatever the initial cost will be, but James Parrott of the Fiscal Policy Institute points to budget surpluses as a possible funding source for one-time retro pay. The city enjoyed surpluses above $1 billion in 15 of the 16 years since 1997, Parrott found in a report this year. Business tax incentives that have tripled to $3 billion since 2001 might also end up on the chopping block.

Alterations to city employee health plans—an area Parrott reports is “ripe for savings”—could come in the form of the union community health centers he advocates for or in contributions from employees, a step supported by the Citizens Budget Commission.

De Blasio will need to employ a combination of these approaches to avoid borrowing the funds. The expired contracts force him to triangulate with care between union leaders supportive of his calls to action on the city’s inequality and budget observers eager for his “fiscal conservative” bona fides. Any new agreements with unions will reveal which side wins out.