If no deal is reached by midnight Sunday, the unions have promised to strike on Monday for the second time in three months, leaving 400,000 riders on the nation's fifth-largest rail system stranded.
"I would say it's a very good possibility. Again, we don't know what's going to happen," ATU president Antonette Bryant said Friday. "None of us want to strike. The bigger deal is that we want a deal and we think there's a deal to be made."
BART General Manager Grace Crunican also joined the discussions Friday after the unions repeatedly criticized her for not being more involved.
"The unions have been clear that they feel that Grace would be helpful in the process," BART spokesman Jim Allison said. "She's been abreast of all of the developments on a daily basis, hourly basis, sometimes."
Bryant said they want Crunican at the table "because she's the dealmaker. She's the one who can say yay, nay or whatever."
BART links far-flung suburbs to bigger Bay Area cities and provides a crucial link between San Francisco and Oakland riders. BART workers went on strike for 4 1/2 days in July, leading to crowded buses, jammed bridges and forcing traffic to a crawl before Gov. Jerry Brown mandated the cooling-off period.
Labor talks initially began in April and have at times been contentious. The two sides have reached agreement on pension contributions but are still at odds over compensation, health care and safety. They would not disclose any specifics citing a gag order by mediators.
The unions want a raise of nearly 12 percent over three years while BART has proposed a 10 percent increase over four years. BART said workers from the two unions now average about $71,000 in base salary and $11,000 in overtime annually. The workers currently pay nothing toward their pensions and pay a flat $92 monthly fee for health insurance.
State transportation officials said they will expand the hours of high-occupancy vehicle lanes should a strike come. BART management has said it would offer limited free charter bus service across the Bay Bridge.