Republicans' periodic bouts of depression over prospects for retaining control of the Senate in this fall's elections can usually be dissipated by a quick glance over the Sierra Nevada mountains.

Out here, in the wellspring of Reagan conservatism and media-dazzle politics, is Sen. Alan Cranston (D-Calif.), the drab, aging symbol of what they feel is an out-of-date liberalism that is supposed to have been driven into the sea.

Their polls tell them Cranston is the most vulnerable Democratic senator up for reelection this fall, threatened by an ascendant GOP and by the possibility that his base of support is wider than it is deep.

Among other things, they say, Cranston's centrist cover -- carefully nurtured by assiduous attention to California industrial, financial and agricultural interests -- has been blown by a "far-out" liberal bid for president in 1984 that was embarrassingly unsuccessful.

They say his middle-ground support may be further diluted by a hot battle to oust liberal state Chief Justice Rose Bird, which could lead to a heavy turnout of conservative voters and a linking of the two because of their opposition to capital punishment, a major issue in the Bird campaign.

Republicans explain away Cranston's previous political successes, including three terms in the U.S. Senate, the longest for a California Democrat, as luck in having weak or outer-fringe opponents who have yielded him the political center.

All it will take to pluck this hardy perennial in the exotic garden of Golden State politics, they contend, is a strong candidate from a united party who does not "scare hell out of the voters," as one GOP strategist put it.

But events of the last few weeks indicate, once more, that this conventional wisdom simply states the problem; it does not necessarily present a solution.

Even Democrats concede that Cranston, 71, would be vulnerable under the ideal conditions cited by the Republicans and could be unseated if Republicans can sort out their problems.

But a half-dozen serious Republican candidates -- or more if you count actor Fess Parker and assorted others who have floated through the race -- have been mauling each other to a standstill in the early stages of a primary campaign that still has four months to go.

And Cranston is back in form as the one of the Senate's most durable long-distance runners, aiming to lock up the election long before ballots are cast. He has fended off Democratic primary opposition despite earlier signs of interest from a couple of House members and San Francisco Mayor Dianne Feinstein, and he has already raised $3.6 million toward the November general election, nearly four times his total at this point six years ago.

"It's a myth, a legend that he's unbeatable," said Rep. Daniel E. Lungren (R-Calif.), who dropped out of the GOP scramble last month after failing to raise enough money. "But he's a tough politician, and you have to work hard to beat him . . . . If I were Alan Cranston, I'd be sitting back and laughing like hell right now."

Smiling maybe, but not laughing and surely not sitting back. He is spending three of every four weekends in the state, phoning when he is not visiting, still collecting money, often as not from mainstream and conservative interests that have bankrolled his earlier campaigns.

"I can't tell you how many offices I've been in where they've said they've gotten three calls from Cranston in the past month," said one of his Republican rivals, U.S. Rep. Edwin V.W. Zschau. Although Zschau and others have put some dents in Cranston's money machine, his contributors' list still "reads like a Who's Who of the Reagan money people," a party strategist moaned.

Zschau, a two-term House member from the San Francisco peninsula's Silicon Valley, is regarded by some national GOP strategists as the strongest threat to Cranston this fall if -- and it is a big if -- he can win the primary. Some Cranston supporters say they agree.

Although Zschau's entrepreneurial, high-tech pitch taps a natural vein in California, he has two fundamental problems. He comes from northern California, heavily outvoted by the more populous south. More importantly, according to some strategists, he has a moderate-to-liberal voting record -- one of the least supportive of Reagan among Republican lawmakers from California.

With the formidable fund-raising aid of David Packard, chairman and cofounder of the Hewlett-Packard electronics firm, Zschau has raised far more money than any other Republican and is beginning to pour it into a major name-recognition effort on television. He said he needs every cent to buy exposure in southern California, where he conceded he is only a "funny name," at best. Moreover, he has recently been moving to the right on some issues, such as casting a proxy vote for military aid to antigovernment rebels in Nicaragua after voting against it last year.

The campaign among Republicans has been dominated in recent weeks by a high-voltage fight between two of the stronger conservative contenders, Rep. Bobbi Fiedler and state Sen. Ed Davis, both of the Los Angeles area, over allegations that the Fiedler camp was trying to bribe Davis to abandon the race with offers to pay his campaign debt. A judge late last month dismissed the charges against Fiedler and her chief aide, citing insufficient evidence and vagueness of the statute invoked in the case.

Political strategists say Davis has been hurt but are not sure about the impact on Fiedler.

"She's the one to watch," said a Republican strategist not connected with any of the campaigns. She is a scrapper, a conservative who has nonetheless taken feminist and other positions that could attract centrist support -- a candidate who, like Zschau, could "give Cranston fits," the strategist said.

The most recently published poll, by the Los Angeles Times after Fiedler's indictment but before the case was dropped, showed the initial beneficiary of the Fiedler-Davis clash to be Los Angeles County Supervisor Michael D. Antonovich.

Antonovich, a former state GOP chairman who has tied himself closely to both President Reagan and Gov. George Deukmejian, quotes the GOP "11th commandment" about Republicans being nice to each other, which has a quaint charm under the circumstances.

Although a staunch Reagan-image conservative, Antonovich positions himself toward the center in relation to another major contender, Bruce Herschensohn, a hard-hitting, acerbic Los Angeles television commentator and former presidential speechwriter during the Nixon administration who has the support and fund-raising aid of Sen. Jesse Helms (R-N.C.).

Other Republican contenders include state assemblyman Robert Naylor, who could cut into Zschau's northern California base, supply-side economist Arthur Laffer and former black activist Eldridge Cleaver, along with a handful of lesser-known aspirants.

Rep. William E. Dannemeyer, who tried briefly to rally antigay sentiment with a plank to exclude acquired immune deficiency syndrome (AIDS) victims from health-related jobs, dropped out. High hopes of Republican leaders to catch an instant front-runner in the form of Peter V. Ueberroth, commissioner of baseball who ran the Olympics two years ago, were dashed when Ueberroth gave them a firm "no" last month.

The June 3 primary battle is more of a swarm than a race, with no one yet emerging as front-runner. The candidates' dilemma was demonstrated recently when Herschensohn put out a flier showing him pulling ahead of other Republicans. He led with 9 percent.