Will Bernie Sanders fight on after Tuesday's primaries?

What next for Sanders and Clinton in Democratic race?

Bernie Sanders says he plans to assess the status of his presidential campaign after Tuesday's primary contests, which could potentially deliver him a win in the critical state of California, where the lion's share of delegates are at stake.

At a campaign event on Monday, he was asked if would consider endorsing Hillary Clinton before the Democratic National Convention in Philadelphia this July.

Clinton hopes for unity as presumptive Democratic nominee

"Well, that's something. First of all, you're asking me to speculate. Let me just talk to you after the primary here in California where we hope to win. Let's assess where we are after tomorrow before we make statements based on speculation," Sanders said.

Sanders said that he'll be in Los Angeles on Tuesday night, then will fly back to Burlington, Vermont and then said he "certainly" plans to campaign in Washington, D.C. ahead of the final primary on June 14. He also said he and his campaign have had private conversations with superdelegates and mentioned that four superdelegates in three or four states might endorse Sanders.

For months, he has maintained that he intends to go all the way to the convention, but pressure is building for him to drop out. Some Democrats fear that it could hurt the party's chances in November if Sanders prolongs the Democratic primary race.

The president spoke with Sanders Sunday by phone for 30-45 minutes, though Sanders declined to characterize the conversation.

In 2008, Clinton dropped out of the Democratic race and endorsed then-Senator Obama a few days after the final primary contests when Obama secured enough delegates to win the nomination.

According to a report Monday in The Wall Street Journal, Sanders' campaign is split over what his next steps should be. Some want him to go all the way to the convention to try and take the nomination from Clinton but others want him to stand down. The report said that Democratic officials, operatives and fundraisers are calling on him to drop out of the race.

On Monday night, Clinton clinched the nomination and became the first woman to top the presidential ticket of a major U.S. political party after securing enough superdelegates, CBS News' Major Garrett reported.

California is among six states that are holding primary contests on Tuesday. In the Democratic race, 694 delegates are up for grabs. California and New Jersey have the most at stake with 475 delegates and 126 delegates, respectively.

While it looks like Clinton will almost certainly win New Jersey, the race between Clinton and Sanders is much tighter in California. A CBS News Battleground Tracker poll released Sunday says 49 percent of Democratic voters in California back Clinton while 47 percent support Sanders.

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