With only 20 days left in the 1984 election campaign, the dark-horse Democratic strategy for capturing the White House is built around a brash attempt at snaring President Reagan's home state of California.

Democratic presidential nominee Walter F. Mondale and his running mate, Geraldine A. Ferraro, plan to spend a disproportionate share of their remaining campaign days in pursuit of California's 47 electoral votes, with Mondale scheduled to visit the state at least twice and Ferraro at least once, a three-day swing next week.

Other evidence of the Democratic commitment here includes a stepped-up media strategy that will put many more ads on the air here than in most other states, according to Joe Trippi, the Mondale-Ferraro state campaign manager.

Surrogate campaigning will be particularly heavy, with Sen. Edward M. Kennedy (D-Mass.) planning to spend five days here and Sen. Gary Hart (D-Colo.), who won the California Democratic primary in June, also tacking up and down the state, Trippi added.

"It's a full-court press in California, no question about it," said John Sasso, Ferraro's campaign manager. "The voters there know Ronald Reagan very well. He's not going to pick up any new votes in California."

When Mondale was reminded earlier this week that Reagan has an unbroken string of election victories in California, the Democrat answered, "He never lost a debate before, either."

A Los Angeles Times poll published today shows Reagan and Vice President Bush leading the Democratic ticket, 53 percent to 42 percent, a narrower margin than the 18-point difference before the first presidential debate Oct. 7.

A California poll also published today by the Los Angeles Herald Examiner shows a similar trend, with the Democrats trailing by 10 points -- 50 percent to 40 percent -- compared with a 16-point spread last month.

The Democrats have coveted California since the campaign began, with Ferraro making her first solo swing here as the vice-presidential candidate Aug. 12. Those aspirations, which were widely belittled at the time, now seem to have a certain unavoidable logic.

With Texas and Florida, the other two major Sun Belt states, looking more and more like Republican strongholds this year, the Democrats have recognized that their chance of victory is almost nil without California. Its electoral votes are 17 percent of the 270 needed to win on Nov. 6.

Mondale and Ferraro appeared in tandem at a $1,000-a-plate, star-spangled gala in Beverly Hills Tuesday night. And Ferraro, making her fourth appearance in California in two months, stumped today in Sacramento and Los Angeles, where she stressed themes that the Democratic strategists believe cut most deeply in this state -- the environment and the war-and-peace issue.

"We're in a fight for peace," she told the California Coalition of Women, using a line that has always played well in this state. "I want a president who has the courage to stand up to the Soviets but also the wisdom to sit down with them and negotiate an arms-control agreement."

The Democrats also have spent heavily on voter registration and get-out-the-vote efforts, trying particularly to harness California's myriad environmental, peace and Hispanic groups, according to senior political adviser Richard C. Leone.

"A win here gives us a huge margin of error for the rest of the nation that we wouldn't have otherwise," said Steven Engelberg, Ferraro's issues director. "If you lose California, then you lose that margin."