SAN JOSE — A new statewide survey shows Democrats Gavin Newsom and Antonio Villaraigosa in a closer than expected race for California governor, with Republicans so far behind that for the first time they may not make the statewide ballot next November.

The survey released Thursday by the Public Policy Institute of California also shows U.S. Sen. Dianne Feinstein leads a fellow Democrat, state Senate leader Kevin de León, by a 2-1 ratio — a testament to the veteran lawmaker’s name recognition across the state.

“Senator Feinstein is leading in the top-two U.S. Senate primary next June — reflecting the incumbent’s favorability rating — while the challenger is not well known,” said Mark Baldassare, president and CEO of the PPIC, who has directed the statewide survey since 1998.

Newsom, the state’s lieutenant governor, leads the governor’s race with 23 percent of likely voters voicing support for him, according to the poll. But it found former Los Angeles Mayor Villaraigosa is quickly catching up — 18 percent of likely voters are backing him. About a third of likely voters were undecided.

Only 9 percent of likely voters chose Democrat John Chiang, the state treasurer, and 3 percent said they’d vote for Democrat Delaine Eastin, the former superintendent of public instruction, according to the poll. Among Republicans, businessman John Cox garnered support from 9 percent of voters. Travis Allen, a state assemblyman from Orange County, received 6 percent, the poll showed.

Under the state’s “top two” primary system, the two candidates who get the most votes in the primary advance to a runoff in November, regardless of party. If the Republican candidates continue to poll poorly, that could mean California for the first time in modern history wouldn’t have a Republican candidate for governor on the November ballot, as in its last U.S. Senate race.

“While these new poll numbers are encouraging, polls don’t distract us from our goal of continuing to organize a powerful grassroots campaign that can help Mayor Villaraigosa win the fight for greater economic opportunity and economic equality,” said Luis Vizcaino, a spokesman for the Villaraigosa campaign.

Newsom’s spokesman, Dan Newman, said he’s “extremely skeptical” about Villaraigosa gaining support given the recent news that the former mayor “made millions lobbying for Herbalife and other shady clients that he refuses to come clean about.”

“While we’re pleased to see yet another poll showing Newsom ahead, we recognize it’s still a long way until the election,” said Newman, “which is why he’s busy traveling the state sharing his vision and record.”

Vizcaino retorted that Villaraigosa is focusing on “lifting more people into the middle class,” while Newsom’s strategy is “apparently to go negative to suppress voter turnout.”

Chiang’s sluggish start in the race is surprising to Jack Pitney, a political science professor at Claremont McKenna College. It could be because his message isn’t resonating with voters yet, he said.

“Maybe he ought to go out and have an affair so he catches up to Newsom and Villaraigosa,” Pitney said. “It’s still early, and he has the kind of approach that could play well on television — a cool, smooth and deliberate manner. As the race plays out, he may be able to move up.”

In the U.S. Senate primary, the poll found that Feinstein — who is seeking her fifth term — leads de León, the state Senate president pro tempore, 45 percent to 21 percent. A third of likely voters are undecided.

Larry Gerston, a professor emeritus of political science at San Jose State, said Feinstein has strong name recognition across the state — unlike de León — and the state senator’s role in the controversy surrounding sexual harassment in the state Capitol could be hurting his campaign.

De León’s housemate, Sen. Tony Mendoza, was accused of inappropriate behavior toward a young female intern, including inviting her to spend the night. The scandal raised questions about how much de León knew about the allegations.

“I think the sexual harassment issue and de León are wrapped together right now,” said Gerston, adding that the Senate leader can win the public’s trust by coming up with solutions such as sexual harassment training, resources for whistle-blowers or more transparency in the State Legislature. “He can either benefit from it in terms of coming up with far-reaching innovative legislation, or he may suffer dearly.”

Courtni Pugh, de León’s campaign manager, said the idea that the sexual harassment scandal might hurt his chances in the race are “nonsense.” She said the numbers merely reflect the current name recognition of the candidates.

“Kevin has been in this race for a little more than a month,” Pugh said. “We knew going in that we would start as underdogs.”

In the governor’s race, Newsom is expected to draw liberal voters with his positions on gun control and his role in legalizing gay marriage in the state. He is largely favored in Northern California. Villaraigosa, preferred by 42 percent of Latino likely voters, will benefit from the moderate and Republican voters. His support base primarily hails from Southern California.

Independents polled by the PPIC preferred Newsom to Villaraigosa 24 percent to 15 percent.

“I like the way Newsom thinks outside of the box,” said Arleen Stanton, 73, a lifelong Democrat and Santa Claran who was polled by PPIC. “I like what he did with gay marriage in San Francisco — he didn’t wait for anyone else to decide. He took the lead on the issue.”

The poll by the nonpartisan PPIC surveyed 1,704 California adult residents who were interviewed on their mobile or landline telephones Nov. 10 to Nov. 19 in English or Spanish, according to respondents’ preferences. Among them were 1,391 registered voters and 1,070 likely voters. The overall margin of error was plus or minus 3.4 percentage points for all adults surveyed, 3.9 points for registered voters and 4.3 points for likely voters.

The PPIC also surveyed voters about hot-button issues like tax reform, the gas tax and affordable housing.

Sixty-two percent of voters oppose the congressional Republicans’ tax plan, which could see a Senate floor vote this week. About 54 percent said repealing the recently enacted state gas tax increase is important to them, while 48 percent said a state bond for affordable housing matters to them.