Ms Brown was last night the front-runner to win today's contest to be nominated as the Democratic candidate for governor of the Golden State - a job once occupied by her brother and her father, which is widely seen as a springboard for an eventual presidential challenge.
But her prospects of winning the run-off in November have paled in recent weeks, and even her campaign workers are privately expressing gloom about her performance to date. She has yet to win over an electorate which is deeply cynical about the political process, and worn down by a lingering recession, earthquakes, fires and riots.
Her fortunes are being followed closely in the US, not least because it could prove to be a significant political triumph for women in their continuing battle to penetrate the male-dominated bastion of politics.
If she wins the governorship, America's most populous state would almost certainly be dominated by a matriarchy of two female senators and a woman governor. At present, Dianne Feinstein, the former mayor of San Francisco, looks certain to be returned to the Senate. She is also up for election in November.
But Ms Brown, the daughter of one of America's most prominent political dynasties, is faltering. According to sources, her once sizable coffers have dwindled from dollars 10m (pounds 6.6m) to less than dollars 1m, forcing her to launch a fresh round of fund-raising.
She has sacked one top manager from her team amid complaints that her campaign was unfocused and after several disputes over slogans. And her opponent, the Republican incumbent Pete Wilson, once the state's most unpopular governor ever, is rallying fast. One recent poll even placed him eight points ahead of her.
Ms Brown would have fared better had she not been ensnared by that most perilous of political issues - the death penalty. Eight out of 10 Californians, weary of a murder epidemic which makes the streets of Belfast look peaceful, favour capital punishment. Ms Brown, who is Roman Catholic, does not, although she insists she will uphold the existing law.
Moreover, she has refused to discuss the issue beyond saying, rather foggily, that her views are a matter of personal conscience. Her opponents are having a field day. One of her two Democratic challengers, John Garamendi, promised to execute all convicted murderers - a job that would require a gassing a day for the foreseeable future. Although he is lagging behind her, his team are hoping for an upset in today's vote.
If she does win the nomination, Ms Brown faces further pounding from Mr Wilson in the next few months.
No one doubts that he will be nominated to run, even though he faces an unexpectedly lively challenge from a 31-year-old right-wing computer millionaire, Ron Unz. Mr Wilson - a former US senator and mayor of San Diego and a protege of Richard Nixon - is a veteran campaigner who knows how to be ruthless.
Although elected as a moderate, he is calling for a fierce clamp-down on illegal immigrants - a cause with a strong populist appeal in California, both to outright racists and to those who merely blame the recession on outsiders. His drum-beating appears to have pushed the Brown campaign to the right, unexpectedy bolstering the popularity of the other Democratic contender for the nomination, Tom Hayden, the former member of the 'Chicago Eight' and an anti-Vietnam radical.
The election is one of a number of primaries across the country today in which candidates will be chosen for five governorships - California, Iowa, South Dakota, New Mexico and Alabama - five US Senate seats, and a plethora of places in the House of Representatives. Although these mid-term elections are a measure of the Clinton administration's popularity, they seem likely to provide rather more evidence about the apathy and estrangement of voters.
California's acting secretary of state, Tony Miller, this weekend predicted the lowest turn-out for a state election since figures were first collated in 1916 - an anticipated 39.8 per cent. The reasons are complex, but seamy accounts of the exploits of the Chicago political muscleman, Dan Rostenkowski, cannot have helped.Reuse content