BART workers hit the polls Tuesday to cast ballots on authorizing a possible strike that would shut down the system as both sides remained entrenched in their positions at the bargaining table.

BART President Tom Radulovich asked Gov. Jerry Brown on Tuesday not to use his powers to request a 60-day "cooling off" period, saying the agency would rather have a strike during the summer when travel is lighter. Governors in the past have used those powers to stave off strikes in 2001 and in the 1990s.

"An unnecessary delay of 60 days would only put off hard choices that will have to be made in order to reach an agreement," BART's letter said. A spokesman for Brown earlier in the day declined comment, saying his office had not received a letter.

The results of the union vote will not be announced until Wednesday morning. If the strike is authorized, as expected, union leaders would have a major card to play just days before the four-year BART labor contract expires at midnight Sunday. The agency's management, however, was not blinking Tuesday, calling the vote just "procedural."

No dates for a possible strike have been set, and an authorization does not guarantee a work stoppage. Workers authorized a potential strike during each of the last three rounds of contract talks -- in 2009, 2005 and 2001 -- but each time they reached a deal before a stoppage. The last strike was a six-day walkout in 1997.

Both management and union representatives briefed reporters Tuesday at separate events in Oakland but mostly reiterated their prior stances and indicated they were no closer to a deal. BART executives mainly want workers to pay more toward their pension and health care plans, while unions are seeking higher wages and safety upgrades.

"We do not want to strike, our members don't want to strike," said John Arantes, president of SEIU local 1021, BART's largest labor unit, which was set to cast ballots up until 10 p.m. Tuesday along with the local Amalgamated Transit Union. He promised to notify passengers of a strike as soon as possible if one is called, but added: "We want to be out there moving our patrons. We will be working hard until the end to get a resolution."

Rick Rice, a BART spokesman, said the results of the vote would not change the agency's approach at the bargaining table.

"We feel there's a deal to be had," Rice said. "Our focus right now is on keeping the negotiations going and the unions working."

Contact Mike Rosenberg at mrosenberg@mercurynews.com or 408-920-5705. Follow him at Twitter.com/RosenbergMerc.