Sala Burton, a small, stocky, brown-haired woman, moved from desk to desk in the cluttered city welfare office, guided by female labor union officials, hailed and embraced by female (and a few male) social workers as she moved toward a political and social milestone.

In a special election today, or if necessary in a Aug. 16 runoff, the 58-year-old widow almost certainly will win the right to succeed her husband, the late representative Phillip Burton, in Congress and turn San Francisco into the first major American city largely led by female elected officials.

The small piece of San Francisco outside the congressional district in which Burton hopes to be elected already is represented in Congress by a woman, Barbara Boxer (D). The mayor, Dianne Feinstein, and the Board of Supervisors' president, Wendy Nelder, are women. Females hold six of 11 seats on the Board of Supervisors and four of seven seats on the school board.

"It's really amazing," said Libby Denebeim, a school board member enthusiastically campaigning along with the rest of the state's Democratic establishment, male and female, for Burton.

San Francisco's remarkable proportion of female leaders means "we have a lot of very humane people in charge," according to Lonnie Weiss, the Service Employees International union local vice president.

San Franciscans disagree about how this has come about, whether it reflects the city's liberal leanings, the large number of homosexuals put off by traditional male politicians or tragic happenstance. Feinstein's male predecessor was murdered; Burton's husband died suddenly April 10 at age 56 of an embolism.

But in Sala Burton, if the warm reception she is receiving is any indication, this old but still fashionable seaport has found someone even more in tune with its cosmopolitan self-image than her husband was.

When Phillip Burton, immersed in the minutia of San Francisco politics, met Sala Galant at a state Young Democrats convention in 1950, he found a politically active young woman who spoke Polish, German, Russian, Yiddish and French. She had been born in Bialystok, Poland, and left in 1939 with her Jewish parents to escape the Nazis.

Phillp Burton became one of the most influential politicians of his time, greatly expanding the National Park System and redrawing California's political map so that Democrats became the dominant legislative party.

When Sala Galant married him in 1953, her career merged with his, but she remained on her own an active organizer of the California Democratic Council, an elected member of several party committees and an active campaigner in her husband's organization.

Michael Novelli, coordinator of Phillip Burton's last campaign and manager of Sala Burton's first, said it was sometimes hard to get the congressman "out and moving around. He used the telephone as an extension of his body." His widow, on the other hand, remains an energetic door-to-door campaigner.

"I want to go everywhere. I want to feel like I've earned this," she said, pausing between campaign stops and speaking with the slightest trace of a European accent.

At the welfare office, she plowed through like a veteran politician, stopping for a lively conversation in Russian with a female case worker who had recently emigrated from Latvia.

Burton's chief concern now, however, is the apathy that threatens the front-runner in any special election.

Her most formidable potential opponents, Supervisor Quentin Kopp and state Sen. Milton Marks, decided not to oppose her. Instead, among her 10 opponents are maverick Republican Gary Arnold, famous for his 1982 shouting match with President Reagan; a Peace and Freedom Party activist; a Libertarian, and a "satirist-wrestler."

Burton's aides list three likely second-place finishers, with perhaps enough combined support to force her into a runoff that she would be almost certain to win. They include Democratic attorney Richard Doyle, 28, who advocates a 5 percent cut in both defense and domestic spending; Republican accountant Tom Spinosa, 60, perhaps the best known because of his losing campaigns against Phillip Burton, and real estate broker Duncan Howard, 42.