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Former Sens. Joe Lieberman and Doug Jones on Sunday faced-off in a debate over the viability of No Labels' potential bipartisan third-party presidential ticket in 2024

Former Sens. Joe Lieberman and Doug Jones appeared Sunday on ABC's "This Week" to debate the viability of a bipartisan third-party presidential ticket in 2024 -- and whether that effort could serve as a spoiler in the race for the White House.

Lieberman, a Democrat-turned-independent who represented Connecticut, is the founding chair of No Labels, which is preparing a possible "unity" ticket that would include both parties and offer, he said, another option for those voters dissatisfied with a potential rematch between President Joe Biden and former President Donald Trump.

"We're in this to give the majority of the American people who feel that the major two parties are failing them a third choice, both in policies, such as we're going to release in New Hampshire [on Monday], but also possibly in a third candidate," Lieberman told "This Week" anchor George Stephanopoulos. "And we've been very explicit ... If the polling next year shows, after the two parties have chosen their nominees, that, in fact, we will help elect one or another candidate, we're not going to get involved."

Jones, an Alabama Democrat and staunch Biden ally who has joined a group to counter No Labels, rejected that thinking.

"Those polls right now mean nothing," he shot back at Lieberman, referencing reticence for both Biden and Trump. "This past weekend, you saw that the Biden-Harris team raised $70 million, 30% of those were new donors," Jones added. "That is not a candidate that is being rejected by the American people.

Of No Labels, he said, "There is no way on God's green earth that they can get to 270 electoral votes, which means they will be a spoiler, one way or another."

Not so, Lieberman insisted. The problem wasn't No Labels, he said. "The problem is the American people are not buying what the two parties are selling anymore. And I think the parties would be wiser to think about that."

Lieberman has experience facing third party bids himself: As the Democratic vice-presidential nominee in 2000, he and presidential hopeful Al Gore lost Florida by a few hundred votes in a state where the Green Party's Ralph Nader got nearly 100,000 ballots, with Lieberman at the time calling any vote for Nader actually a vote for opponent George W. Bush.

The dueling views on No Labels come amid Democratic handwringing over whether the group's plan -- which it says would comprise of one Democrat and one Republican on the same ticket next year -- is more likely to peel off disaffected Republican voters who would vote for Biden in a pure head-to-head with Trump next year.

Lieberman said Sunday that No Labels would hold off on its campaign if Democrats and Republicans both embrace centrism.

"We have said all along that we're not yearning to run a third-party ticket. If one or both parties move more toward the center in their policies ... and maybe think about the two candidates being so unpopular among the American people, we won't run," he said.

Jones said there was already a more moderate option available in Biden, noting the president's cooperation with Republican lawmakers in Congress.

"Look at what he has done, bringing the infrastructure package together, pulling that together for the first time in decades to do infrastructure, for the PACT Act [for veterans], the CHIPS Act [for manufacturing]," Jones said.

"I don't know why in the world somebody thinks that Joe Biden's administration is so far left, unlike a Donald Trump or someone else that is an extreme right," he argued.

In interviews and public statements, the group has repeatedly insisted that while polling proves there's an appetite for a third option in 2024, No Labels would take an "off ramp" if they are wrong.

"That sort of runs against human nature, doesn't it? Once a campaign starts, it's hard to stop," Stephanopoulos pressed Lieberman on "This Week."

"The American people don't like what the two parties are doing," Lieberman responded. "And they particularly don't like the two candidates that they seem set on nominating."

Jones, however, took issue with No Labels largely operating outside of public scrutiny.

"They're not disclosing their donors. They're not playing by the same rules," he said. (A No Labels spokesperson previously told ABC News: "We never share the names of our supporters because we live in an era where far-right and far-left agitators and partisan operatives try to destroy and intimidate organizations they don't like by attacking their individual supporters.")

Jones on Sunday criticized how No Labels might also put together its ticket -- not through a series of public primaries but through back-room discussions that undercut the very pitch Lieberman was making.

"That's not very democratic. That's not a choice," he said. "It's a false choice and really an illusion as to what they're doing."

Even some Republicans have cast doubts on No Labels' viability, pointing to past failures by third-party candidates to make a legitimate run at the White House. The group has also faced roadblocks in its effort to get access to the ballot in all 50 states.

"I think it’s a fool’s errand. ... I’m not in this for show time. I’m not in this, you know, for making a point. I’m in this to get elected president of the United States," former New Jersey Gov. Chris Christie, who is running for the White House as a Republican, said on "This Week."

"And there are only two people who will get elected president of the United States in November of '24 -- the Republican nominee for president, and the Democratic nominee for president."