WASHINGTON, 15 August 2003 — President Bush arrived in California yesterday with his political fortunes increasingly tied to the powerful but unpredictable figure of Arnold Schwarzenegger.

Bush has kept a distance from the Oct. 7 ballot drive to remove Democratic Gov. Gray Davis from office, and he has declined to endorse the movie-star and bodybuilder who has overnight become the leading Republican and most popular candidate on the ballot. “He would be a good governor, as would others running,’’ is all Bush would say Wednesday, tempering earlier remarks that appeared to favor Schwarzenegger.

For better or worse, however, a number of Bush aides, Republican strategists and pollsters believe the Terminator’s fortunes in the recall, if only because of his dominating presence in the race, will affect the president’s re-election prospects next year in the nation’s most populous state — and possibly beyond.

One prominent adviser to Bush said the excitement behind the muscle man’s candidacy means “California’s not lost forever.’’ On the other hand, said GOP strategist Scott Reed, “If Arnold flames out after this historic buildup, it’ll look like Republicans can’t get their act together.’’

“Like it or not, the Bush White House is a little pregnant on the Arnold candidacy,’’ Reed said.

In the best scenario for Bush, Davis is ousted, Schwarzenegger triumphs with a united Republican vote and California’s bleak fiscal situation begins to improve. With the governorship in popular Republican hands, the state’s 54 electoral votes, once a lost cause for the GOP, could come within Bush’s grasp in 2004.

Alternatively, if Schwarzenegger’s candidacy implodes, it could leave the Republicans without an obvious candidate to face reinvigorated Democrats. And Schwarzenegger’s candidacy could turn the vote into a referendum on racial politics, because he supported an immigration crackdown in 1994 that continues to infuriate Hispanics. Such a backlash could hurt Bush beyond California in 2004.

Bush’s aides and advisers are caught between the potential risks and rewards. Though rumors swirl about involvement in the Schwarzenegger campaign by Karl Rove, Bush’s top strategist, the White House is officially mum. “I haven’t asked anybody to get engaged and I’m not aware of anybody that has been engaged,’’ Chief of Staff Andrew Card said Wednesday.

The White House finds itself in the awkward position of playing spectator in a race that could alter Bush’s political future. Though Rove cares so much about California that an associate calls the state “Karl’s Ahab,’’ the recall was driven by people at odds with the administration such as Shawn Steel, who was pushed out by Bush allies as state party chairman. “It changes the fortune for the presidential campaign dramatically if we win,’’ Steel said.

A Bush adviser acknowledged that “the recall was not something that we wanted to happen because it potentially gives the Democrats a chance to say what’s happening in California is all about the recall process and not about the governor and his Democratic leaders.’’ The adviser said Bush’s 2004 prospects would be hurt if Davis, or Democratic Lt. Gov. Cruz Bustamante, prevails and performs well in office, or if a Republican wins and does poorly in office. “There is fear that, beloved this year, the (new Republican) governor could be unpopular next year,’’ said a Bush campaign official. “Maybe it’s better to keep Gray Davis as a punching bag.’’

Still, Schwarzenegger’s decision to join the race, and early polls showing broad support, have buoyed the Bush campaign’s hopes of a lift in 2004. “Schwarzenegger is the only candidate who has a chance to achieve what we wanted,’’ said one adviser, adding that the two leading conservatives in the race, businessman Bill Simon and state Sen. Tom McClintock, have too much of a “hard edge’’ to add to Bush’s appeal in the state.

Don’t expect Bush to say that publicly, however. Bush aides believe that appearing to meddle would backfire and boost Democrats’ efforts to link the California recall to the Florida recount. Still, California Republicans say, lawmakers and others tied to the White House have been putting what one called “heavy pressure’’ on Simon and McClintock to drop out — and one GOP strategist close to the White House expects one or both to quit.

The recall effort has already produced some benefits for Bush. It has frozen the Democratic nominating contest in a desirable spot for Bush — with no obvious challenger to Bush. The attention to California is also depriving the Democratic candidates of attention and is expected to cramp their fund-raising.

Also, George “Duf’’ Sunheim, who became chairman of the state GOP earlier this year, said the recall has already boosted Republican voter registration, a potential benefit to Bush next year. “Whatever excitement there is will wear off, but the impact on registration will lasting,’’ he said.

Even if a Republican governor does not deliver California to Bush next year, Republicans believe it would make Democrats spend more time and effort to win the state. “We can distract the opposition long enough to make them vulnerable elsewhere on the national political landscape,’’ said Dan Schnur, a California GOP operative.