Bernie Sanders Bernie SandersKenosha will be a good bellwether in 2020 Biden's fiscal program: What is the likely market impact? McConnell accuses Democrats of sowing division by 'downplaying progress' on election security MORE could pull off a win in next week's California primary, with a new poll showing the White House hopeful ahead by 1 percentage point.

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A USC Dornsife/Los Angeles Times poll released Thursday evening shows Sanders leading with 44 percent to Clinton's 43 percent.

Sanders's 1-point lead falls within the poll's margin of error.

California's primary is open to independent voters that give Sanders a boost; among registered Democrats, Clinton still leads Sanders by 4 points, while Sanders has 50 percent support from independents to Clinton's 34 percent.

But, the poll found, Clinton has a 10-point lead among those likely to vote next week, primarily due to support from older voters.

Sanders has continued to close the gap between him and Clinton and has been campaigning hard across the state.

“Bernie Sanders has tapped into a wellspring of support in the Democratic primary over the last several weeks and he’s closing with a rush,” said Dan Schnur, director of USC’s Jesse M. Unruh Institute of Politics, which partnered with the L.A. Times to conduct the poll.

"If Clinton manages to hold him off and win the primary, it would be as a result of a low turnout that tilts the electorate in her direction."

Sanders has barnstormed California in recent weeks, hoping to grab a large share of the state's 475 pledged delegates up for grabs. However, if primary results are as close as recent polls indicate, Sanders and Clinton would split the 475 delegates evenly, which wouldn't give the Vermont senator much of a boost in his search for the nomination.

Clinton leads Sanders in the pledged delegate count 1,769 to 1,501. When superdelegates, the unbound party leaders who vote at the July convention, are factored in, the former first lady's lead blossoms to 2,313 and puts her just 70 delegates short of the Democratic nomination, according to The Associated Press delegate tracker.

Sanders has pledged to fight up until the Democratic National Convention to convince superdelegates to flip and hopes a convincing win in California will help.

The Los Angeles Times poll is just the latest to show it will be a close race for the two Democratic candidates.

A Field poll released Thursday morning showed Clinton leading Sanders by just 2 points, 45 percent to 43 percent, among likely Democratic primary voters.

And a NBC/Wall Street Journal/Marist poll released Wednesday similarly shows Clinton and Sanders within 2 points of each other: Clinton leads Sanders 49 percent to 47 percent in that poll.

The LA Times poll surveyed 1,500 voters from May 19-31 and has a margin of error of 2.9 percentage points. That included 903 Democratic voters, with a margin of error of 3.7 percentage points, and 503 likely Democratic voters, with a margin of error of 5 points.