By Eric Bradner

CNN

PHOENIX (CNN) -- As Democrats choose their next national party leader, the candidates vying for the job acknowledge one thing awaits the winner: A major credibility problem.

The still-lingering tensions of the 2016 primary have dominated the contest so far to head the Democratic National Committee. But they have also masked the deeper problem: After a year of debate scheduling drama, hacked emails, questions about impartiality and former Chairwoman Debbie Wasserman Schultz's convention-eve resignation, many Democrats aren't convinced the DNC is even capable of playing a central role in the party's Donald Trump-era resistance.

For backers of Bernie Sanders, the DNC isn't viewed as an honest broker. And on Hillary Clinton's side, the organization is seen as so beset by controversy that it might be more trouble than it's worth.

Evidence of Democrats' distrust is already evident: Sanders has so far declined to share his massive fundraising list with the DNC, and former attorney general Eric Holder is heading a major new Democratic redistricting initiative, separate from the DNC.

Within the race for DNC chair, Minnesota Rep. Keith Ellison, Labor Secretary Tom Perez and five other candidates broadly agree that the party needs to invest deeply in state parties and in working-class America, that it needs new efforts toward protecting voting access and that the next chair must be a more successful fundraiser.

First, though, even the contenders for chair acknowledge that the DNC must re-establish its credibility.

"Listen, the DNC is now a weaker organization coming out of this election than it was going into it," Jaime Harrison, the South Carolina Democratic chairman and one of the seven candidates to helm the DNC, said Saturday in an interview with CNN at the first of four "future forums" the party is holding.

"The question is how do you get it back on track? We're in the ditch -- how do we get it out of the ditch and then back on the road?" Harrison said. "I can understand the hesitation on people's parts and the hand-wringing that is going on -- because all of the things that took place in this past election were just really hard, and the hits just didn't stop."

Clinton-Sanders tensions felt

The candidates for DNC chair have largely rejected the characterization of the race as a Sanders vs. Clinton proxy battle -- in part because Ellison doesn't want his support limited to Sanders supporters and Perez knows he can't win without some backing from the party's ascendant progressives.

But those tensions are evident in the race: Sanders has not committed to sharing his massive fundraising list with the DNC -- saying he wants to make sure it isn't diluted through use to bolster candidates that don't meet his progressive standards. That lack of a show of faith has angered many Democrats and threatens to hobble Ellison, who Sanders has endorsed.

Perez, meanwhile, has aligned himself closely with President Barack Obama -- but his core argument for the job is that he can address the problems that languished during the Obama years.

"The task ahead is the task of being a fixer-upper-in-chief, and I've prided myself on being the turnaround guy in the work that I've done," Perez said.

He has offered a series of technical fixes -- starting with a unit dedicating to protecting voting access -- and says he could restore the party's lagging morale.

"When people don't have a hop in their step when they get out of bed in the morning," he said, "they're not as productive."

Perez said Democrats need an "honest broker" who runs a "transparent ship" and is "never in fact or in perception putting their thumb on the scales" in primaries, he said, to rebuild party loyalists' faith in the DNC as its central institution.

"We have to earn it. We have to show people that we can do it," he said.

More than nuts and bolts?

Ellison, meanwhile, rejected the importance of helming the DNC as a nuts-and-bolts fix-it job.

"The top priority's not a nuts-and-bolts thing. And I know reporters and Washington political types -- they just want to go to the nuts and bolts. But the most important thing is attitudinal," Ellison said.

"We didn't arrive where we are because we got nuts and bolts wrong. Nuts and bolts flow from core motivation and purpose," he said. "If you get purpose right, everything tends to flow in the right direction after that. It's amazing how easy things become after you get the purpose right."

Pete Buttigieg, the mayor of South Bend, Indiana, entered the race late and is basing his candidacy on the rejection of a second Sanders-against-Clinton battle -- and on the argument that as a local official, he could shift the party's focus away from Washington.

"One of the things you could sense in the crowd, right, amongst the DNC members, is they don't feel connected to the mother ship," he said.

Buttigieg said that for the next DNC chair, "the fundraising role is huge," and that "we need the buy-in and the investment from Democrats in every part of the country."

But, he said, the DNC is an organization badly in need of a new chief executive.

"We don't seem to have any kind of strategic plan -- we just go from one cycle to the next," he said. "We've got to just do the bread-and-butter, how do you run the organization right, before we can really get into any of the spiffy innovation things that I want to do."

Ray Buckley -- a long-time New Hampshire Democratic chair, floated the idea of "co-chairs" leading the DNC -- with one focused on presenting the party's message on TV and the other handling the internal, technical challenges. That idea didn't gain traction, so he entered the race himself. Buckley said the party's handling of the 2016 race was deeply flawed.

"The very first thing I'd do is address the issues that came to light in the nominating process: the neutrality of the chair and the staff; superdelegates; the joint fundraising agreement; how the caucuses are just so wildly different from one state to another and there's no support; and the debate schedule," he said.

"None of that had to happen," Buckley said. "None of it."