(CNN) The leading Democratic candidates for president made strong appeals to African American voters Wednesday night -- particularly women -- as they drew a direct line between re-creating the coalition that elected Barack Obama in 2008 and defeating President Donald Trump in 2020.

Debating in a Deep South state where black voters will likely be the majority of the Democratic electorate in the March primary, the discussion over who could best represent that community drew the most fireworks in an otherwise civil debate among the 2020 candidates Wednesday in Atlanta. Questions from the MSNBC/Washington Post moderators on the thorny topic of race drew charged exchanges between New Jersey Sen. Cory Booker and former Vice President Joe Biden, as well as South Bend, Indiana, Mayor Pete Buttigieg and California Sen. Kamala Harris.

The debate struck at the core of the electability argument taking place within the Democratic presidential primary. Both Booker and Harris, the two black candidates on stage, argued that Democrats must nominate a candidate in 2020 who understands the issues facing those communities if the party intends to activate and bring out enough voters on Election Day to defeat President Donald Trump. Booker pointedly noted that Hillary Clinton underperformed with black voters in key battleground states in 2016 -- one of major factors that led to her loss to Trump.

In doing so, they made implicit criticism of Buttigieg, who has emerged as a front-runner in the key state of Iowa, and who has struggled to attract support from black voters. Biden's solid support from black female voters, who have so often been the linchpin for successful Democratic nominees, has bolstered his standing in the polls, particularly in states like South Carolina.

But Booker, Harris, Buttigieg and Massachusetts Sen. Elizabeth Warren all sought to loosen his grip on that key constituency Wednesday night, which led to some of the most interesting contrasts between the candidates and an embarrassing misstatement by Biden that underscored concerns among Democrats about his readiness to face Trump.

Booker led off that exchange by aggressively challenging Biden's recent statement that he will not yet support legalizing marijuana, because he wants further study on whether it is a "gateway drug."

"I thought you might have been high when you said that," Booker said to the former vice president. "Marijuana in our country is already legal for privileged people. The war on drugs has been a war on black and brown people. So let me just say this: With more African Americans under criminal supervision in American than all the slaves since 1850, do not roll up into communities and not talk directly to issues that are going to relate to the liberation of children."

Defending his position, Biden got tangled up in his words.

"I come out of the black community in terms of my support," Biden said, and then began listing his support from three former chairs of the black caucus and "the only African American woman who's been elected to the Senate" -- alluding to former US Sen. Carol Moseley Braun, but seeming to overlook the presence of another black female senator: Harris.

"No, the other one is here," Harris responded from the other end of the stage, laughing and spreading her arms out in disbelief.

Harris made her case for the nomination by arguing that she could recreate the Obama coalition -- using a question about the recent controversy over the Buttigieg campaign's use of a stock photo featuring a woman from Kenya on his website to suggest that other candidates are not as tapped into the issues of the black community.

"For too long candidates have taken for granted the constituencies that have been the backbone of the Democratic Party," Harris said. "They show up when it's close to election time -- show up in a black church and want to get the vote -- but just haven't been there before."

"At some point, folks get tired of just saying 'Oh, thank me for showing up' and say 'Show up for me,'" Harris said, noting that black women have far higher rates of maternal mortality, more children lost of gun violence and get paid 61 cents on the dollar compared to all women who make 80 cents on the dollar.

"The question has to be where have you been and what are you going to do?" Harris said.

Buttigieg, whose struggle to attract black support is the greatest weakness of his candidacy so far, said he welcomed the challenge of connecting with black voters in America. "My faith teaches me that salvation has to do with how I make myself useful to those who have been excluded, marginalized, and cast aside and oppressed in society," he said.

"While I do not have the experience of ever having been discriminated against because of the color of my skin, I do have the experience of sometimes feeling like a stranger in my own country, turning on the news and seeing my own rights come up for debate, and seeing my rights expanded by a coalition of people like me and people not at all like me," Buttigieg said.

Buttigieg registered at 0% support from black voters in one recent poll in South Carolina. That could be a major stumbling block in early contests that will be dominated by black voters. In the 2016 Democratic primaries, CNN exit polls showed that the black vote factored heavily in the outcome in many of the early states in the south. Black voters made up 61% of the electorate in South Carolina; 54% in Alabama; 51% in Georgia; 32% in Tennessee and 32% in North Carolina.

As Buttigieg has surged in the polls in the kickoff stage of Iowa, he is also facing more scrutiny of his record and relative inexperience in government. MSNBC moderator Andrea Mitchell noted in one question that he won his mayoral election with fewer than 11,000 voters and lost his only race for statewide office by 25 points. "Why should Democrats take the risk of betting on you?" Mitchell asked Buttigieg.

Buttigieg argued that he doesn't have "traditional Washington experience" but that Democrats need a nominee who can go toe-to-toe with Trump, "who actually comes from the kinds of communities that he's been appealing to."

"I also wore the uniform of this country and I know what is at stake in the decisions that are made in the Oval Office and the Situation Room. I know from the perspective of Washington what goes on in my city might look small," he said, but "the infighting on Capitol Hill is what looks small; the usual way of doing business in Washington is what looks small."

The disjointed beginning to the debate bounced from subject to subject, and was marked by two candidates -- businessmen Tom Steyer and Andrew Yang -- going nearly 30 minutes without being asked a question.

Minnesota Sen. Amy Klobuchar attempted to answer one of the central questions often raised by Democratic voters: whether a female nominee can vanquish Trump after he defeated Hillary Clinton in a heated 2016 campaign charged with sexism.

Klobuchar, in an attempt to put any concerns to rest on that topic, had one of her strongest moments of the debates so far.

The Minnesota senator was asked to defend her recent comments to CNN's Jake Tapper that women are held to a higher standard -- and that a female candidate with Buttigieg's experience would never have made the debate stage.

Klobuchar said she was honored to stand on stage with Buttigieg, but then turned the point to her advantage by arguing how a woman could win against Trump in 2020.

"Women are held to a higher standard," she said. "We have to work harder and that is a fact."

In a stand out moment, Klobuchard quipped, "I govern both with my head and my heart, and if you think a woman can't beat Donald Trump, Nancy Pelosi does it every single day."

Earlier in the debate, the ongoing impeachment inquiry into Trump took center stage of the debate on Wednesday following a blockbuster day of testimony on Capitol Hill.

Two of the candidates who may end up having a say in Trump's eventual fate, Sens. Warren and Klobuchar, were among the first to weigh in on the proceedings in Washington.

Using the impeachment hearings to advance her argument that government has been corrupted by money, Warren opened the debate questioning how wealthy Republican donor Gordon Sondland -- the star witness in Wednesday's hearing -- won his ambassadorship to the European Union.

Warren said Sondland's testimony shows "the corruption, how money buys its way into Washington." Donors should not believe they are entitled to ambassadorships, she argued.

"I'm taking a pledge," she said, asking others on stage to join her. "Anyone who wants to give me a big donation, don't ask to be an ambassador, because I'm not going to have that happen. ... We are not going to give ambassador posts to the highest bidder."