House Democratic leaders are worrying about the role Vermont Sen. Bernie Sanders still has left to play in the general election even as they insist that their party will unite behind presumptive Democratic nominee Hillary Clinton.

Shortly after meeting with Clinton on Capitol Hill Wednesday, party leaders were asked whether it's a big problem for Democrats that Sanders still has yet to endorse Clinton, and that a recent poll indicated that many Sanders backers remain on the fence about supporting her. The June poll, conducted by Bloomberg Politics among likely general election voters, found that only a little over half of Sanders backers -- 55 percent -- actually planned to vote for Clinton.

"That is a problem for the party," South Carolina Democratic Rep. Jim Clyburn said at a press conference. "I would love to see Mr. Sanders endorse -- go all in. And I think he will."

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Clyburn said he believed Sanders will announce his endorsement "in the not too distant future."

"It may be he wants to do it at the convention, whatever it is," he added. "But I've looked at my Congressional district, where he had a tremendous following among young people. I have yet to find a single one of those young people who has said to me that he or she will not vote for this nominee."

Questioned whether there was anything Clinton could do to encourage Sanders' supporters, California Democratic Rep. Xavier Becerra said the presumptive nominee addressed the issue during their meeting.

"She's going to go out there and talk to everyone in America," Becerra said. "Not just Sanders supporters, but she's going to talk to those who aren't supporting the Democrats. Because as she said, she's going to be president for everyone."

He expressed his faith that Sanders backers would eventually turn to Clinton in the general election.

"Quite honestly I believe not just Sen. Sanders but Sen. Sanders' supporters as we get closer to November will look closely at this race and make some really strong decisions to support the most qualified person to be president," Becerra said. The California congressman later said he was unaware whether he was being vetted for a vice presidential slot.

Democrats also sought to highlight the differences between themselves and the Republican party when it comes to supporting their respective presumptive nominees.

"You saw the stark contrast," House Minority Whip Steny Hoyer said at the press conference, noting some Republicans' reluctance in backing Trump due to the billionaire's inflammatory rhetoric and controversial policy proposals. "Unity versus disorganization, lack of confidence in the other party in their leader."