The parties held talks Monday after the unions backed off a threatened strike deadline late Sunday and gave Bay Area Rapid Transit managers a 24-hour reprieve.
By late afternoon both sides appeared to remain firm in their positions.
BART's board president urged the unions to let its members vote on the agency's final offer that was presented Sunday.
A union leader urged BART to tweak its offer.
Pete Castelli of the Service Employees International Union Local 1021 said "it will take a hail Mary to prevent a strike" and that commuters should prepare for that possibility.