ATU President Antonette Bryant said the unions were anxious to see the offer. She reiterated that the unions do not want to strike.
If the clock strikes midnight with no agreement, workers could walk off the job, stranding an estimated 400,000 rail commuters. Last July, BART workers struck for 4 1/2 days, leading to jammed bridges and roadways, and crowded buses throughout the Bay Area before Gov. Jerry Brown mandated the cooling-off period.
On Wednesday, union leaders thought they had a deal with BART management but said the proposal presented late Tuesday was rescinded.
"We thought we were really close and they totally yanked it off the table," Bryant said. "We gave them a counteroffer, and the next day they said, 'Oh, you misunderstood what we proposed.' We said, 'No we didn't.'"
Hock said BART never made a formal offer and blamed a mediator for the confusion.
"The mediator misunderstood and miscommunicated what had been talked about because we had never put that offer out there in any way, shape or form," Hock said.
The two sides have reached agreement on pension contributions but are still at odds over compensation, health care and safety.
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 pay a flat $92 monthly fee for health insurance.
On Monday, union leaders declined to give the public the customary 72 hours' notice before a strike. The unions said they didn't provide the notice because they wanted to leave every possible option open for a resolution.
During the talks, BART officials unveiled a $21 million contingency plan to give commuters more options, including free charter buses, extra carpool lanes and even limited train service run by managers.