One of the most important primaries for governor this year takes place on Tuesday in the Golden State where Democrats run everything. The race offers Republicans a chance to begin rebuilding their image in the state as the party of economic opportunity for all.

Republicans are presented with starkly contrasting candidates in former Bush Treasury official Neel Kashkari, a son of Indian immigrants, and Assemblyman Tim Donnelly, who led the Minuteman campaign to patrol California's southern border and has likened illegal migrants to jihadists. Mr. Donnelly has staked his campaign on appealing to Republican voters for whom cultural conservatism and opposition to immigration are the main lodestars. But that electorate hasn't come close to being a state majority for decades, and those views risk alienating the growing share of minorities and unaffiliated voters, many of whom share the GOP's economic views.

Minorities made up 41% of California's electorate in 2012, up from 34% as recently as 2008. More independents than Republicans cast ballots in 2012, a flip from prior presidential elections. GOP voter registration has fallen by 7.5 percentage points to 28.7% since 1997 while the share of unaffiliated voters has risen by nine points to 20.9%. Republicans are becoming fewer and less relevant, a trend Mr. Kashkari hopes to reverse.

Some Republicans have written off Mr. Kashkari because of his stewardship of the bank bailout while at Treasury, though the real policy sins were those that led to the housing mania and panic. Like a majority of Californians, he's also a cultural liberal. Yet this makes him more attractive to a large swath of voters who would never consider a candidate who opposes same-sex marriage and abortion. That includes many young people and Silicon Valley techies.

Mr. Kashkari is also focusing on economic opportunity, especially for the poor. The political rookie has reached out to voters in the rural Central Valley and inner-cities where he is making the case that broad-based economic growth and education reform can redress California's inequality and poverty.

California ranks fourth in unemployment (7.8%) and has the nation's highest poverty rate (24%). Yet unemployment in the Bay Area is nearly two-thirds lower than in the Central Valley and much of Los Angeles. California fourth graders rank 46th in the country in reading and math, and since 1980 its graduation rate has slipped to 48th from 11th.

Mr. Kashkari has sketched out a jobs and education plan, which neither Mr. Donnelly nor Governor Jerry Brown have bothered with. He wants to streamline California's education code, eliminate the statutory cap on charter schools and ensure that charters have equal access to resources and facilities a la New York. He's also proposed a 10-year sunset on regulations and a $250,000 cap on non-economic personal injury awards.

Credit Mr. Kashkari for his nerve in challenging Mr. Brown, who will be hard to beat. Yet also at stake this November is the state legislature where Democrats won a supermajority in 2012, allowing them to unilaterally raise taxes. Republicans stand a shot of regaining their veto on taxes by flipping three Assembly seats in Bakersfield, Los Angeles and Orange County. All three districts have a plurality of Latinos.

Five Democratic Congressman including Reps. Ami Bera (Rancho Cordova), Scott Peters (San Diego), Raul Ruiz (Inland Empire), Jim Costa (Fresno) and Jerry McNerney (Stockton) also are vulnerable this year. Mr. Kashkari offers an optimistic candidacy that could add buoyancy rather than drag at the top of the GOP ticket.