It's not often a politician is so popular that people want to buy his spit. But a cough drop purportedly used and then discarded by California Gov. Arnold Schwarzenegger--and retrieved from a trash can--was fetching more than $15,000 late last week on eBay. "I was kind of disappointed," Schwarzenegger joked to NEWSWEEK. "I thought it would go for $100,000."

It's not hard to see why many California Republicans regard Schwarzenegger--rather George W. Bush--as the GOP's hottest star of 2004. After presenting a balanced budget, Schwarzenegger's approval rating is 65 percent--and it has soared among independents and Democrats. But rather than putting California "in play," as optimistic Republicans predicted when Schwarzenegger won last year's recall election, many now fret that the nation's most populous state is a lost cause for Bush, or at best what a White House official calls "a tough challenge, still." In an interview with NEWSWEEK, Schwarzenegger sympathized with the toll Iraq has taken on Bush's popularity and said comparing him with the president was "a big mistake." But he also cautioned he can do little to improve Bush's standing. "It is totally up to him and his team," says Schwarzenegger. "If the people in California feel that the president loves this state, pays attention to this state, he's really serious about wanting to win this state, is catering to this state... they will respond accordingly."

So far, that doesn't appear to be the case. Schwarzenegger and Bush haven't spoken to each other since March--and Bush has no plans to visit California any time soon. Schwarzenegger served on the elder President Bush's Physical Fitness Council and reveres "41," but he and the current president have little rapport. Schwarzenegger's advisers say he has little patience for White House strategist Karl Rove, whom the governor blames for tepid support in the recall--and for not taking seriously Schwarzenegger's pet cause: after-school programs. (The two also tangled at the 2000 GOP convention over a speech Schwarzenegger wanted to give, and jockeyed over who would appear first on "Larry King Live"--Rove won.) And Rove reportedly was not pleased when Schwarzenegger drew a longer reception line than the president at a governors' meeting in February--and is determined that Schwarzenegger "doesn't cast too big a shadow" at the party's convention in New York this August, says one GOP strategist.

Schwarzenegger has been coy about how much of his star power he plans to lend to the convention. He will "most likely" be there, he says, before adding, "with great enthusiasm." But aides are also already arranging his schedule so that he can claim to be busy in Sacramento if they sense the convention is adopting a harsh partisan tone that could diminish Schwarzenegger's appeal in California.