LOS ANGELES  Meg Whitman, the Republican candidate for governor in California, passed a milestone the other day, investing $119 million of her own money into her campaign, breaking a record held by Mayor Michael R. Bloomberg of New York.

But Ms. Whitman is the latest wealthy Californian to learn that it may take more than money to win an election here, particularly for a first-time candidate confronting a vast and convoluted electoral landscape. With a month to go until Election Day, Ms. Whitman is struggling against a Democrat, Jerry Brown, who, after spending most of his career in public office, had been seen by Republicans as the best opponent Ms. Whitman could have asked for, given voters’ frustration with the state’s dysfunctional government.

Ms. Whitman’s most recent problem emerged as she sought to explain this week how she had employed for nine years a Mexican housekeeper who was an illegal immigrant. Ms. Whitman has been an advocate of penalties against employers who hire illegal immigrants. But she said she had not known of the housekeeper’s illegal status until the woman informed her last year, and she sought to provide documentation to back up that claim.

The episode has proved a distracting embarrassment that has raised questions about Ms. Whitman’s credibility and has threatened to derail a key element of any strategy to win election in a largely Democratic state: appealing to Latino voters. As she has sought to explain what happened, Ms. Whitman said she had fired the housekeeper on the spot, even as she described the maid as a close part of her family, and seemed undisturbed by the idea that her onetime friend and employee might be deported.