As Democratic Gov. Edmund G. Brown gears up his campaign for the presidency, his administration is plunged into such political turmoil that his ability to govern California effectively may be threatened.

Over the last three weeks, three of Brown's vetoes have been overridden by the Democratic-controlled legislature, the most ever against a California governor in modern times.

Brown also found himself snubbed by the University of California's Board of Regents, who refused to adopt his widely publicized proposal to ban nuclear weapons reasearch at the university's Lawrence Livermore laboratory. And on top of that, the Senate here rejected his appointment of actress Jane Fonda, a key political ally, to the state Arts Council, a move the governor and Fonda denounced as "small-minded McCarthyism."

"He's never been too popular with the legislature but now it's even worse," said Sen. Alfred Alquist, the Democrat who led the battle to override vetoes of two pay raises for state employes in recent weeks. "These overrides show a growing disenchantment with him. I think it shows his general ineffectiveness and his inability to govern."

The overrides of the pay raise vetoes have been particularly galling to the governor and his aides, who plan to make fiscal responsibility one of the catchwords in their coming attempt to dump President Carter. $&(WORD ILLEGIBLE

Some Brown staffers openly admit that the precedent-smashing rebukes in recent weeks may have been largely engendered by the legislators' widespread personal dislike for the governor and resentment of his ambition.

In trying to block the $220 million pay raise, Brown had proposed smaller increases for state workers, who received no raises last year in the wake of Proposition 13. The 80,000-member California State Employes Association (CSEA) successfully demanded retention of the full 14.5 percent voted by the legislature.

"They beat us on this because they really exploited the anti-Brown fervor around here," said Marty Morganstern, director of the governor's office of employe relations. "Without this they couldn't have gotten as far."

Brown's chief of staff, Gray Davis, insists the veto overrides have not undermined his effectiveness. By granting the pay increases, Davis maintains, the legislature showed itself to be out of touch with post-Proposition 13 realities.

"We're fighting for what we believe in and we're confident the public will be outraged by these increases," Davis said. "I think this is more of a test of CSEA's strength than the governor's strength. This is precisely the type of thing that invites the arbitrary constraints of a Proposition 13 initiative or a balanced budget constitutional amendment."

Brown lashed out at the regents' refusal to ban nuclear weapons work at Lawrence Livermore, describing his own position as a "prophet against the tide, for life and against death." He criticized the Senate's rejection of the Fonda appointment as "an insult to the very idea of artistic excellence."

Despite the governor's rhetorical blasts, many Sacramento observers believe the real reason for these setbacks is that Brown has, after four and a half years in office, finally lost his political magic. Many legislators now see him as hopelessly aloof and arrogant, refusing to work seriously with them.

"Brown won't be able to veto a damn bill this year," said a high-level Senate staffer. "All the kids Jerry's been bullying are seeing him stumble. Now they're all piling on. He has no loyalty from anyone around here. He's shot his wad."

Perhaps the most immediate factor contributing to Brown's problems on the home front, many here believe, is his impending run for the presidency. There seem to be few enthusiasts here, outside his immediate staff, for Brown's challenge to President Carter, who is also unpopular but is more distant and doesn't stir the kinds of emotions the governor does.

Senate Republican leader William Campbell, a staunch Brown ally on the pay-raise veto, blames the governor's lack of popularity for the overrides. He says that in his own lobbying of Senate Democrats, Brown support was more a liability than an asset.

"There are a lot of votes cast around here recently just to embarrass Jerry Brown. He has problems on both sides of the aisle. He plays to an audience other than the state and that annoys people," Campbell said. "You have a lot of Teddy Kennedy supporters here, you have Jimmy Carter supporters. I don't see many Jerry Brown supporters. People are doing what they can to stop him and help their man."

Staff chief Davis denies that the overrides and other setbacks of recent weeks have anything at all to do with presidential politics. While admitting that "friction and additional tension" is developing between legislators and governor, Davis sees no serious damage to Brown's ambitions.

"This has nothing to do with the presidential thing," Davis said. "We don't worry about it "cause" we feel we're doing what the majority of the population is for." CAPTION: Picture, Gov. Brown: A critic says "kids Jerry's been bullying are seeing him stumble. Now they're all piling on.", UPI