A high-stakes dispute between unions and the developer of the Concord Naval Weapons Station is threatening to derail the Bay Area’s biggest housing project, a 13,000-unit redevelopment of the former military base in Contra Costa County.

For more than a year, the developers have been in talks with the building trades unions over how much of the $6 billion project’s construction would be done by union workers. But those discussions are at an impasse. The Contra Costa Building Trades Council is insisting all the work at the 5,000-acre site be done by union members. The developers, Lennar Concord LLC and FivePoint, are arguing that such a deal, called a project labor agreement, would kill the project because it would lose money.

The developers said that agreeing to an all-union job site would make the project infeasible, raising construction costs by $542 million and cutting profits from 17% to a loss.

The long-simmering conflict boiled over into public view during a six-hour hearing Tuesday night at the Concord City Council. The council must determine whether Lennar and FivePoint are complying with a 2016 agreement that requires the developers to “negotiate in good faith to secure one or more project labor agreements” for the project’s construction.

After more than 100 members of the public weighed in Tuesday, the City Council voted to continue the hearing to Wednesday night. But on Wednesday night, faced with the choice of backing labor or potentially killing the development, the council did neither. Instead, it ordered the two sides back to negotiations.

The council also included a grab bag of non-binding guidelines for the two sides to consider while negotiating. The list, mostly items the union had asked for, includes the developer paying prevailing wage and providing a training program.

Kofi Bonner, co-chief operating officer for FivePoint, said Wednesday in the wake of the council’s request “indeed I am a little confused.”

“I’m not sure this gives us guidance to get over the impasse,” he said. “One wonders how one goes forward.”

Already the project has been stalled. Two months ago, the development team suspended work on the project and stopped paying $37,000 a month to the city for staff work on the weapons station because of the labor dispute.

Vice Mayor Dominic Aliano lashed out at developers over their decision to stop making the $37,000 monthly payments to the city.

“People can interpret that in different ways, but to me it’s sending the community the middle finger,” he said.

Council member Edi Birsan, who made the motion to send the two sides back to talks, declined to weigh in on whether developers had been negotiating in good faith with the unions.

“I don’t want to address bad faith or good faith,” he said.

At Tuesday night’s hearing, residents appeared evenly divided on the massive development, which will shape the future of the diverse city of 120,000 that lies 29 miles northeast of San Francisco.

Housing advocates spoke of the 3,000 affordable homes the project would deliver to Concord, which produced just 2% of its state-mandated affordable housing goals. Youth sports coaches praised the extensive sports complex and playing fields that the project would include. Business boosters said that the project’s 6 million square feet of office space, clustered near a BART station, could become a tech hub perfectly positioned to capture overflow from San Francisco and Silicon Valley.

Matt Regan of the Bay Area Council, a pro-business group, called the development “the most significant project in our region in our lifetime.” He said that Concord’s commercial and residential rents are not high enough to support union wages similar to those paid in San Francisco, which has much higher rents.

“You can negotiate with the unions. You can negotiate with Lennar. But you can’t negotiate with math,” he said. “Math is math.”

The more than 40 union workers who showed up Tuesday — ironworkers, sprinkler fitters, electricians — spoke of the city’s “Concord first” policy, which requires big projects to pay living wages, hire local workers and source materials from local businesses. They said that an agreement would mean those on the job would be able to afford to live in Concord. The unions’ apprenticeship program would benefit thousands of blue-collar Concord young people, who could earn a living wage in their backyard.

“When you decide to use a PLA, what you are doing is deciding to make an investment in your community,” said Jason Lindsey, an ironworker. “You’re giving (Concord residents ) the opportunity for a quality middle-class life.”

Building Trades Council attorney Dan Cardozo said that filling the job site with nonunion workers would mostly attract workers from the Central Valley, “taking jobs from local people, driving down area wage standards and depriving the local economy of the multiplier effect” of having local residents earning money that will be spent in their own community.

At the heart of the debate was whether the developers had promised a comprehensive agreement in 2016 when they were picked for the development. Labor representatives said that Bonner seemed to agree to an all-union project at that time.

“There was no misunderstanding on what they were going to do as far as a PLA,” said former Contra Costa County Building Trades President Greg Feere, who was involved in the early talks with Lennar. “They seemed like bobble-head dolls. They just nodded their heads.”

Bonner said he never promised that the entire project would be governed by a single agreement, but that he expected to have different deals with different unions. He expects that there will be about $1 billion in union work in phase one.

Bonner said his group is “responsible for the overall economics of the project,” which Concord is counting on to generate significant tax revenue. He added that his group is committed to spending $310 million before the first dollar of revenue is generated.

Retired Concord police Sgt. Scott Wagner urged the two sides Tuesday to come to a compromise, arguing that the city’s future depends on the weapons station development.

“Either Concord will be become a preeminent city in the East Bay,” he said, “or the city that just couldn’t make it happen.”

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com Twitter: @sfjkdineen