James P. Bradley is a Coast Guard veteran, an MBA holder and chief financial officer at a heath care startup, but he’s just been thrust into his biggest role yet — the GOP’s best hope of vying for a Senate seat in deep-blue California.

The primaries are Tuesday, and the state’s unusual “jungle” system means the top two vote-getters, regardless of party, advance to the general election. A University of California, Berkeley Institute of Governmental Studies poll on Friday said Mr. Bradley is “within striking distance” of second place.

Sen. Dianne Feinstein, the incumbent, is likely to come out on top, but Mr. Bradley is hoping to nip state Senate leader Kevin de Leon, a Democrat who is hoping to make the general election an all-Democratic affair.

“I’m gonna pull it off,” Mr. Bradley told The Washington Times. “I pray every day on this and I’m still in the race. I really feel strongly about this.”

Ms. Feinstein tops the 32-candidate field with 36 percent in the new poll, while Mr. de Leon is second at 11 percent and Mr. Bradley takes 7 percent.

Eyeing an upset, Mr. Bradley is banking on Republican fence-sitters to coalesce around him instead of divvying their vote among eight other GOP candidates, as Mr. de Leon struggles to draw Democrats away from Ms. Feinstein.

Mr. de Leon is widely seen as the biggest threat to Ms. Feinstein, a 84-year-old Capitol Hill veteran. He’s already exhibited some clout, nabbing big endorsements from labor unions and swiping more delegates than Ms. Feinstein at the party convention in February.

The latest polling suggests he’s got a mountain to climb in the general election, but only if he can survive a Tuesday scare from his closest GOP challenger.

Berkeley says a whopping 38 percent of Republicans are undecided in the final week of the primary campaign, compared to 20 percent of Democrats, heaping pressure on Mr. de Leon to dig up votes....

“The highly partisan nature of voter preferences and the fact that nearly twice as many Republicans as Democrats are still undecided, could work to Bradley’s advantage since it offers him greater opportunities than de Leon to expand his support base in the closing days,” the Berkeley pollsters said.The California primary features nine Republican candidates in all, and none of them have spent a lot of money or built up name recognition.Mark DiCamillo, director of the Berkeley IGS poll, said picking a Republican candidate is “really like shooting darts” for party-line voters.“For Bradley, my sense is they see this kind of noncontroversial Anglo name that benefits him, and his job title — chief financial officer — benefits him,” Mr. DiCamillo said.Mr. Bradley doesn’t contest the theory. “I think it’s that, as well as the fact I’m not a politician. People are tired of politicians. We’ve seen the results in California,” he said. “They want a citizen to go in there that has the professional experience that

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