Democratic US presidential candidate Bernie Sanders at a campaign rally in Salem, Oregon, on May 10. Reuters/Jim Urquhart Bernie Sanders is closing in on Hillary Clinton in California, according to a new poll.

Clinton leads the Vermont senator by just two points among likely Democratic voters — 49% to 47% — according to a Wall Street Journal/NBC News/Marist poll released on Wednesday. The difference falls within the poll's margin of error.

Sanders is depending on a victory in California on June 7 to keep his slim hopes for the Democratic nomination alive. California offers 475 pledged delegates, the biggest haul of any state.

Clinton can secure enough delegates for the nomination next week even without winning California, thanks to the superdelegates who have already pledged to support her.

But a loss in the nation's biggest state could underscore Sanders' case that superdelegates should switch their support to him ahead of the Democratic National Convention in July. He could also use a victory in California to push for more influence on the party's platform.

Like other Democratic primaries, California splits its delegates proportionally, so a close victory by either candidate will do little to change the delegate math.

The poll does bring some good news for Clinton, though: She leads among people who voted early by 58% to 41%.

Earlier this week, Clinton scored a key endorsement from California Gov. Jerry Brown, who said that Clinton was "the only path forward" to defeating the presumptive Republican presidential nominee, Donald Trump.