One of California’s most prominent Republicans says she is voting for John Cox and urged Orange County GOP Assemblyman Travis Allen to “support the front-runner” in the governor’s race or “drop out.”

Harmeet Dhillon, a San Francisco attorney who is a member of the Republican National Committee and a frequent guest on Fox News, noted that recent polls show Cox with a narrow second-place lead over Democrat Antonio Villaraigosa in the June 5 primary. Both men are trailing Democrat Gavin Newsom, the polls indicate. The top two finishers, regardless of party, will advance to the November election.

Dhillon said she has donated money to Allen’s campaign and likes both him and Cox, but worries that outnumbered California Republicans will split their vote in the primary.

That could result in a two-Democrat runoff in November, which in turn could be disastrous for national Republican hopes of holding the House. Several competitive congressional seats are in California, and GOP turnout in the fall could be depressed without a Republican candidate in a marquee contest such as the governor’s campaign.

“Since it is not numerically possible for Travis to make it into the top two — something that we Republicans really need for the down-ballot — it’s time for all Republicans to support the Republican front-runner, including Travis Allen,” Dhillon wrote wrote in a Facebook post Wednesday night. “He can be a spoiler, or he can be a gracious future candidate and a hero. #Unite.”

In another post, Dhillon urged Republicans not to be fooled by mailers being sent by an independent expenditure committee backing Villaraigosa that tout Allen. The goal of the independent group: to split the Republican vote so Villaraigosa can advance into the top two.

“I supported Travis before, but he can’t win this one. I hope I can support him again for another race in the future,” Dhillon wrote. “Meanwhile, he should disavow these sleazy ads from Republican-haters designed to fool the voters, and drop out so he isn’t a spoiler.”

Cox, a San Diego County businessman who has run for office several times but never won, secured President Trump’s endorsement last week. He has also been endorsed by House Majority Leader Kevin McCarthy, R-Bakersfield.

Allen, who has been endorsed by more than 20 Republican county committees in California, doesn’t sound like he’s considering backing Cox. He responded to Dhillon on Thursday by saying, “Unfortunately, the establishment Republicans are once again selling out Californians.

“Our polling shows us in a tight race to make the top two and advance into the November election,” Allen said in a statement. “Apparently, the party elites have learned nothing from failing with (former GOP gubernatorial nominees) Meg Whitman, Neel Kashkari and Arnold Schwarzenegger, and are now propping up a four-time failed Chicago politician that’s favored by Gavin Newsom and the (Service Employees International Union).”

After Trump endorsed Cox, Allen tweeted, “The political establishment misinforming @realDonaldTrump is now actually scared of a TRUE CONSERVATIVE GOVERNOR in California. There is ONLY ONE Californian that can beat @GavinNewsom and the CA Democrats.”

Joe Garofoli is The San Francisco Chronicle’s senior political writer. Email: jgarofoli@sfchronicle.com Twitter: @joegarofoli