Assemblyman Tim Donnelly (R-Twin Peaks), center, scares California Republican strategists. (Rich Pedroncelli/AP)

Top California Republican strategists are becoming increasingly nervous about a race the party almost certainly cannot win.

There is little hope that whichever Republican makes it through the Golden State’s top-two primary June 3 can beat Gov. Jerry Brown (D). The state’s economy is rebounding, revenues are surpassing expectations, Brown’s approval ratings are strong and his campaign war chest is flush with cash.

But Republicans are concerned by Assemblyman Tim Donnelly (R), an arch-conservative who takes a hard line on social issues, especially on immigration, and has a penchant for making offensive statements.

With Donnelly at the top of the ticket, party strategists worry that he will drag down other Republicans running for office in November, further damaging the GOP brand in a state where Democrats enjoy near-super majority status.

Polls show Donnelly outpacing former Bush administration official Neel Kashkari (R) for second place in the top-two primary. The most recent Public Policy Institute of California survey, conducted the second week in April, showed Brown leading all candidates with 46 percent of the vote; Donnelly took 9 percent, while Kashkari clocked in at just 2 percent, below the poll’s margin of error.

The fight for the right to lose to Brown matters because Republicans and Democrats are battling over a handful of contested U.S. House races, too. Republicans are aiming to knock off Reps. Ami Bera (D), Julia Brownley (D), Raul Ruiz (D) and Scott Peters (D), while Democrats hope to beat Rep. David Valadao (R) and win back seats held by retiring Reps. Gary Miller (R) and Buck McKeon (R).

Republicans are also hoping to make gains in critical state Senate and Assembly districts. In the Senate, Democrats won a super majority in the 2012 elections, but they lost that advantage after three of their members were suspended over criminal investigations into their activities.

When Brown beat former eBay executive Meg Whitman (R) by 13 points in 2010, he lost several of those districts. Republicans believe they can compete if Brown wins again, even by 20 points. But if Brown faces Donnelly and wins by a wider margin, he could pull Democrats across the finish line in those down-ballot races.

National Republicans have rushed to Kashkari’s aid. Karl Rove on Friday told conservative radio host Hugh Hewitt that a Donnelly win could damage the party nationwide.

“If the California Republican Party has as the leading candidate, the leading statewide candidate on the ballot this year somebody who has said the outrageous things that he’s said and prone to the outrageous behavior that he routinely engages in, it will be used to tarnish not only the California Republican Party, but they’ll throw it at everybody else on the ballot, and everybody else will, across the country, disavow the guy,” Rove said. “Every time he goes out and says something, and as we’ve seen, Mr. Donnelly is quite prone to sharing the weird recesses and corners of his mind, it could be really problematic for the GOP.”

Former governor Pete Wilson (R), who backed an anti-illegal immigration initiative that set the California party back with Hispanics a generation ago, issued his own warning against picking Donnelly.

“With Tim Donnelly on the ballot, it would be a losing campaign, risking injury to our party and our state, and to other Republican candidates who deserve to win,” Wilson wrote in a letter.

Wilson has joined former Massachusetts governor Mitt Romney, former secretary of state Condoleezza Rice and former Florida governor  Jeb Bush in backing Kashkari in recent weeks. On Friday, Kashkari’s campaign said the candidate had loaned himself an additional $1 million for the final stretch run, the second big check Kashkari has written himself.

No matter how off-putting voters find Brown’s opponent, the Democrat isn’t likely to match the previous best electoral performance for a California governor. Back in 1946, Earl Warren earned both the Democratic and Republican nominations; he won with more than 91 percent of the vote.