Hillary Clinton has the high-profile backers, the lead in delegates and the well-funded organization, yet she is still in danger of losing Tuesday’s Democratic primary in deep-blue California, a loss that would send her limping into the party’s nominating convention.

The Clinton campaign on Sunday expressed confidence heading into California, where the former first lady won in 2008 over Barack Obama. But the campaign is also downplaying the contest and stressing that Mrs. Clinton already is the Democratic Party’s presumptive nominee despite a tougher-than-expected challenge from Sen. Bernard Sanders.

“Well, I think if you look at the popular vote, if you look at the majority of pledged delegates, I should have captured those by Tuesday, but I’m going to keep fighting hard here in California and in the other states that are voting on Tuesday because I want to get as strong a vote as I possibly can,” Mrs. Clinton said during an interview on ABC’s “This Week” program. “But I think given where we are in this race, that I will have not only more than a 3 million-vote margin, but I will have a significant majority of pledged delegates by the close of voting on Tuesday.”

Polls show a close contest in California. The most recent Real Clear Politics average of all surveys has Mrs. Clinton up by about 5 percentage points — a smaller margin than expected, given her strong support by virtually all of the Democratic Party establishment in the state.

California Gov. Jerry Brown and Sens. Dianne Feinstein and Barbara Boxer have publicly backed Mrs. Clinton, as have a number of other prominent Democrats in the state. Yet the former secretary of state faces the prospect of losing to Mr. Sanders in the nation’s largest state.

Such an outcome would add fuel to Mr. Sanders‘ plan to fight all the way until the Democratic National Convention in July, even as presumptive Republican nominee Donald Trump can focus on unifying his party and honing his attack lines for the general election. Mr. Sanders is far behind in the delegate race, but he argues that his continued strong showings — along with the fact that he performs better against Mr. Trump in hypothetical November matchups than does Mrs. Clinton — should make the party think twice about nominating Mrs. Clinton.

He also contends that a win in California could lead party superdelegates to switch sides and abandon Mrs. Clinton at the convention.

“We’re going to win. If the turnout is very, very large, I think we have a chance to win big,” Mr. Sanders said of the California contest before turning his fire on the party leadership and its assumption that Mrs. Clinton will be the eventual nominee.

“We don’t know what the world is going to be like four weeks from now, five weeks from now,” he said on CNN’s “State of the Union” program. “Let’s not forget, the Democratic convention is at the end of July. That’s a long time from today.”

Mr. Sanders also hopes that a surge in California voter registration aids him and is banking on new voters to support him. About 650,000 Californians registered to vote in the past 45 days, bringing the state’s total voter registration to a record 17.9 million.

“This presents us with a golden opportunity — we think a big percentage of those new voters are ready to support Bernie,” the Sanders campaign said in an email to supporters Sunday.

In addition to California, Democrats in Montana, North Dakota, New Jersey, New Mexico and South Dakota also will go to the polls Tuesday. It’s a virtual certainty that, even with a loss in California, Mrs. Clinton will emerge from Tuesday’s slate of primaries with the needed 2,383 delegates to officially claim the Democratic nomination.

As of Sunday, she had 2,316 delegates to Mr. Sanders‘ 1,547, according to an Associated Press tally. The figures include superdelegates, 547 of whom back Mrs. Clinton compared with 46 for Mr. Sanders.

There are 548 delegates at stake in the California primary. Of those, 475 will be awarded through voting, though the party’s proportional allocation system means Mr. Sanders would have to win by a big margin to make any sizable dent in Mrs. Clinton’s lead.

The other 73 are superdelegates. Of those, at least 61 have come out in favor of Mrs. Clinton. There has been little indication that superdelegates, who include top party officials and local elected leaders, are willing to switch sides and join Mr. Sanders.

Sanders keeps on fighting

Despite that, the senator from Vermont is unwilling to scale back his attacks on Mrs. Clinton, even as the former first lady has tried to turn virtually all of her attention to the looming battle with Mr. Trump.

On Sunday, Mr. Sanders attacked Mrs. Clinton’s foreign policy record and said he fears she would be too quick to lead the nation into war if elected president.

He was asked on “State of the Union” if he worries Mrs. Clinton could push the U.S. into war.

“I worry about that, yeah, I do,” he said. “I think her support for the war in Iraq was not just an aberration. I think her willingness to kind of push President Obama to overthrow [Libyan strongman Moammar] Gadhafi [that led] to the kind of instability that we’re seeing now in Libya, not inconsistent with her other views in Syria, where she wants a no-fly zone which could suck us into never-ending conflict in that area.”

Mr. Sanders was an outspoken opponent of the Iraq conflict, while Mrs. Clinton voted to approve the war in 2002. She has since said her vote was a mistake.

Even in light of the apparent bad blood between the two sides, Clinton campaign officials say they will be prepared as early as Wednesday morning to begin trying to bridge the divide and unite Democrats.

Clinton campaign Chairman John Pedestal said on “Fox News Sunday” that he won’t call on Mr. Sanders to quit the race even if he loses California. But the Clinton campaign, he said, will change strategy after the primaries.

“We’re not telling Bernie Sanders what to do. He needs to make up his own mind about that,” Mr. Podesta said. “We’re going to do everything we can to reach out to his supporters and to him directly.”

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