Their latest potential champion is of vintage political stock. She is Kathleen Brown, the daughter of Edmund 'Pat' Brown and sister of Jerry 'Moonbeam' Brown - the maverick Democratic presidential candidate. If elected, she would be the third Brown in four decades to govern California, a job regarded as a springboard for a run at the White House.
Her success would be another victory for women nationwide, who are celebrating the acquisition of several top jobs in the Clinton administration and a stack of new seats in Congress. And it would be still more of a triumph at state level, following the election of women - Dianne Feinstein and Barbara Boxer - to California's two Senate seats.
In the past two months Ms Brown, at present the state treasurer, has been raising large sums of money. Although she has not formally declared her intentions, there is little doubt in political circles that she will go for, and get, the Democratic nomination for the state's top political job, which is up for election in 1994.
As things stand, she has an excellent chance of victory. She is bright, moderate and politically astute; she performs well on television; and is well connected in Wall Street and Hollywood, important sources of campaign funds. Most importantly, unlike her eccentric brother, she is well- liked in the Democratic Party. Her father, a towering figure in Californian politics who was governor during the boom years of 1958 to 1966, has described her as the 'best politician in the family'.
Jerry Brown, who served two terms as governor, from 1974 to 1982, could be a potential embarrassment to her, because of his reputation for whackiness. He has taken to the wilderness for a period of contemplation, but his political career is unlikely to be over.
His sister's position is greatly assisted by the miserable fortunes of California's governor, Pete Wilson, a Republican, who is still trying to recover after a disastrous election year. So far his governorship has been spent surviving a series of crises. These include the state's dollars 11bn ( pounds 7bn) budget deficit, the Los Angeles riots, several sizeable earthquakes, a six-year drought, a plague of medfly, and a series of huge forest fires.
Matters have been made worse by a recession which, according to some economists, may not begin to ease until 1994. Mr Wilson is also deeply disliked by a large chunk of the Republican right who resent his pro-choice position on abortion and believe he is soft on homosexuals.
But these are early days. The last time California voted for a Democratic president was in 1964, when it elected Lyndon Johnson. Two years later, a Republican won the governor's race - a former 'B-movie' actor who later spent eight years in the White House.