Poll: Trump's lead just 1 point in California
© Greg Nash

Republican presidential front-runner Donald TrumpDonald TrumpTrump to undo Obama's climate change agenda Kushner met Russian bank executives: report Trump tweets: 'Trump Russia story is a hoax' MORE holds a razor-thin lead over rival Ted CruzTed CruzConservatism's worst enemy? The Freedom Caucus. Republicans giving Univision the cold shoulder: report How 'Big Pharma' stifles pharmaceutical innovation MORE in California, according to a new USC Dornsife/Los Angeles Times statewide poll.

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.