Atlanta (CNN) For all the marches and protests the left has generated since Election Day, the debate over who will lead the Democratic Party in the early stages of Donald Trump's presidency is underscoring the divisions still lingering within its ranks.

Eight candidates to become the next Democratic National Committee chair -- led by former Labor Secretary Tom Perez and Minnesota Rep. Keith Ellison -- struggled during a debate sponsored by CNN Wednesday to define a vision of how they would effectively counter Trump's administration and break through in clear opposition to his message.

Perez and Ellison, recently spotted dining together, said they didn't cut any deals ahead of the 447 DNC members' vote for chair Saturday in Atlanta and pledged to confront Trump with a unified party. But the debate showed the party hasn't settled questions over just how vigorously to oppose Trump, or how to settle division within its own ranks.

Ellison said Trump's actions so far "legitimately raise the question of impeachment." He said Trump has already violated the Constitution and called for an investigation to "make sure that nobody can monetize the presidency and make profit off it for our own gain."

"We have seen from the get-go that this person wants to turn the clock back, and the Democratic Party needs to take the fight to Donald Trump," Perez said. "When we lead with our values, when we lead with our conviction, that's how we succeeds."

But another candidate cautioned against focusing too much energy on Trump.

Pete Buttigieg, the mayor of South Bend, Indiana, called Trump a "computer virus in the American political system."

"Yes, we've got to take the fight to him. But we can't let him dominate our imagination, because it's our values and our candidates that matter," he said.

Central challenge

Another central challenge for Democrats is to recover from the bitter split of the 2016 presidential primary. The wounds of that race were ripped open at the debate over a question about whether the race between Sanders and Hillary Clinton was "rigged."

After Perez sought to avoid directly answering the question -- saying the party had lost trust in its voters and created a "crisis of relevance" -- long-shot candidate Sam Ronan, an Air Force veteran from Ohio, jumped in to call the contest rigged and say Sanders' supporters felt excluded at the Democratic convention in Philadelphia.

Buttigieg said Democrats don't want to make the mistake of reliving the 2016 race.

"We can't allow this to devolve into factional struggle," he said.

The candidates also broke over future primary contests.

Jaime Harrison, the South Carolina Democratic Party chairman, issued a stern call on party members not to launch primary challenges against the 10 Democratic senators in states that Trump won in 2016.

He said Democrats would find themselves in a "permanent minority" because the GOP needs just seven more Senate seats for a filibuster-proof majority there, and just one more statehouse to call and control a constitutional convention.

"We don't have the time, the energy -- and all the people we are fighting for each and every day don't have time for these purity tests. We have to fight back against the Republicans; we can't fight against each other," Harrison said.

His comments come after a liberal group called "We Will Replace You" was launched, threatening primary challenges to Democrats who don't oppose Trump at every stop.

Other contenders, meanwhile, said the DNC shouldn't stand in the way of primary challenges. Perez said that "the role of the DNC chair is to let the process run its course." Ellison said that while he'd make private calls, "the role of the DNC is to be neutral and fair to all primary contestants."

At the forefront

Perez and Ellison are at the forefront of an eight-candidate field. Perez is picking up the endorsements of the heads of the Democratic National Committee's caucuses for women, Hispanics, Asian-Americans and rural Americans. Ellison is picking up the mantle of the insurgency that fueled Sanders' presidential run. Buttigieg, meanwhile, got the backing of former DNC chairman Howard Dean.

Aides and vote-counters for several candidates say they believe Perez -- who says he has commitments of support from 180 of the DNC's 447 voting members -- has a narrow lead over Ellison. But both sides admit they don't yet have the votes necessary to clinch the job.

It could turn other contenders -- especially Harrison, Buttigieg and Idaho Democratic Party executive director Sally Boynton Brown -- into kingmakers. Television analyst Jehmu Greene and Wisconsin lawyer Peter Peckarsky are also in the running.

Perez rolled out his latest endorsements Wednesday from leaders of four DNC groups in a statement first obtained by CNN.

"Tom is committed to ensuring the DNC not only listens to diverse voices from all states and territories but will include the diverse members of the DNC in rebuilding the organization and elect Democrats everywhere," said Bel Leong-Hong, chair of the DNC's Asian American and Pacific Islanders Caucus.

"He knows that in order to fight back against Trump and Republicans, we must unite as Democrats. He knows that we can't just organize at a church every fourth October, we must organize 12 months a year," said Iris Martinez, the chair of the DNC's Hispanic Caucus.

DNC Women's Caucus chair Lottie Shackelford and DNC Rural Council chair Betty Richie are also supporting Perez.

"We need a DNC chair who is committed to listening to voters and communicating our message to both urban and rural areas, and Tom is committed to doing that," Richie said.

Outsider gaining steam

Buttigieg picked up an endorsement Wednesday morning from Dean, the former Vermont governor and DNC chair whose famed "50-state strategy" is the model each of the candidates in the current race say they believe the party needs.

Buttigieg has positioned himself as a break from the Sanders vs. Clinton proxy battle -- with Ellison backed by Sanders and Perez supported by many Clinton allies -- that the DNC race has become.

Ellison got a surprising endorsement of his political acumen on Wednesday morning in the form of a tweet from the President.

"One thing I will say about Rep. Keith Ellison, in his fight to lead the DNC, is that he was the one who predicted early that I would win!" Trump tweeted.

One thing I will say about Rep. Keith Ellison, in his fight to lead the DNC, is that he was the one who predicted early that I would win! — Donald J. Trump (@realDonaldTrump) February 22, 2017

Ellison had already gained a key supporter over the weekend when New Hampshire Democratic chairman Ray Buckley dropped out and urged his supporters to back the Minnesota congressman.

It was "a real momentum-builder" in Ellison's favor, said Michael Kapp, a DNC member from California who backs Ellison.

"Ray has been on the DNC for a long time, and more than anyone else, has a deep knowledge base of how the DNC has operated in the past and what needs to be changed," Kapp said.