Thursday night's 2020 Democratic presidential debate was "really important" because moderates came out on top this time, pollster Lee Carter said Friday.

Appearing on "Fox & Friends" with host Pete Hegseth, Carter -- partner and president at Maslanksy and Partners -- said that progressives had a really hard night, but cautioned voters to "really focus" on independents.

"Because, that's what's going to carry whoever is going to win the White House," she noted. "It's not going to be just the partisan divide."

According to Carter, younger candidates businessman Andrew Yang and Indiana Mayor Pete Buttigieg had the best nights. Both candidates challenged extreme progressive stances. Carter showed the real-time reactions to the debate from groups of Democrats, Republicans and independents, including a testy exchange between Buttigieg and Sen. Elizabeth Warren.

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In a blunt one-on-one sparring match over fundraising, Warren, D-Mass., threw the first punch, hitting Buttigieg for his recent lavish fundraiser in Napa, Calif., saying he was cavorting with "billionaires in wine caves" -- prompting Buttigieg to retort that Warren, a multimillionaire, was a populist in name only.

"You know, according to Forbes magazine, I'm literally the only person on this stage who is not a millionaire or billionaire," said Buttigieg. "This is the problem with issuing purity tests you yourself cannot pass."

Democrats, he argued, are "in the fight" of their "lives," and need all the support they can get -- whether from the wealthy or otherwise. He added that he'd gladly accept a donation from Warren if she were to offer one.

Just minutes later, Yang slammed Democrats for their "obsession" with President Trump and impeachment.

"The media networks didn't do us any favors by missing the reason why Donald Trump became our president in the first place," Yang told the PBS Newshour moderators. "The more we act like Donald Trump is a cause of our problems, the more Americans lose trust that we can actually see what's going on it our communities and solve those problems."

"What we have to do is we have to stop being obsessed over impeachment," he stated.

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Carter agreed with Yang, telling Hegseth that she believes voters are "exhausted" by impeachment.

She told Hegseth that while she doesn't think it's going to change for Yang in the polls, she believes Buttigieg will see a "little bit of a surge" as a result. Carter said that voters seemed to side with Buttigieg during his confrontations with Warren, with Democrats and independents giving him an "A" grade.

The next debate will be held on Tuesday, January 14, 2020, at Drake University in Des Moines.

Fox News' Paul Steinhauser, The Associated Press, and Gregg Re contributed to this report.