Republican presidential front-runner Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE holds a razor-thin lead over rival Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE in California, according to a new USC Dornsife/Los Angeles Times statewide poll.

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Among likely June primary voters, Trump leads Cruz by just 1 point, 36 to 35 percent. John Kasich falls far behind, at 14 percent.

Trump, however, got 30 percent support among registered Republicans surveyed in California, according to the poll. Cruz got 30 percent and Kasich received just 12 percent support.

Low turnout could hurt Trump and help Cruz, the Times reported.

According to the poll, about 25 percent of California Republican voters said they would refuse to vote for Trump if he is the Republican Party's nominee.

In all, about 75 percent of voters who were surveyed in California had an unfavorable view of Trump. Among Republicans, 43 percent had an unfavorable impression, while 51 percent had a favorable view of the front-runner.

The poll was conducted by phone with 1,503 registered voters in California from March 16 to 23. The margin of error for all voters was 2.8 points. The margin of error for Republican primary voters is 5.5 points.

According to the RealClearPolitics average of polls, Trump leads Cruz by 10.7 points in the state. He has 33.7 percent support compared to Cruz who has just 23 percent. Kasich has 16.3 percent.

The California primary will be held June 7.