Earlier this morning, the ATU put out a statement saying the mediator told both sides they couldn't leave until a deal was done because they were extremely close to a deal. Talks lasted more than 16 hours and wrapped up around 5:45 a.m.
"The bargaining has produced some constructive and productive progress," said Cohen.
When asked about the possibility of a strike tomorrow, Cohen only reiterated that trains will be running normally today.
Both sides are now under a gag order.
Sticking points in the 6-month-old negotiations include salaries and workers' contributions to their health and pension plans.
BART General Manager Grace Crunican said a "last, best and final offer" presented to the unions Sunday was $7 million higher than a proposal presented Friday. It includes an annual 3 percent raise over four years and requires workers to contribute 4 percent toward their pension and 9.5 percent toward medical benefits.
Crunican said the unions had two weeks to accept the deal before it would be taken off the table.
The unions said the parties were about $16 million apart over four years.
Politicians try to help sides avoid strike
About 10 politicians have been involved in the effort to avoid a BART strike, not in the negotiating sessions, but on the sidelines pressuring both sides to compromise. They have been quietly working behind the scenes, but they made their presence known over the weekend.
"We have two missions: keep the trains running and keep the discussions going," Assm. Nancy Skinner, D-Berkeley, said.
John Logan, the head of San Francisco State University's labor and employment studies program, says the politicians were neutral observers trying to pressure both the unions and management.
"It would not have been useful to have them there all along, but just to try to push the deal over the finish line, which regrettably did not happen," Logan said.
Unions and democratic politicians have long had a cozy relationship. According to figures from Maplight.org, between 2010 and 2012, SEIU has given more than $2.5 million to state lawmakers and ATU has given more than $300,000.
But Logan believes constituent distress over a possible strike holds more sway than money.
"I think their intervention was extremely helpful and extremely necessary," he said.
And as the clock ticks down, San Francisco Mayor Ed Lee has postponed his scheduled trip to china to work the phones hoping to help forge an agreement.
Stay with ABC7NEWS.COM for updates on the looming BART strike and information on how to get around if the trains stop running. Follow us on Twitter, Facebook, and Google+ and download our news app for the latest news whenever and wherever you want.
Bay City News, the AP, and ABC7 News reporters Matt Keller, Laura Anthony, John Altson, Wayne Freedman, Carolyn Tyler contributed to this story.