WESTERVILLE, Ohio — Sen. Elizabeth Warren got a first taste of what it is like to be the front-runner on the debate stage Tuesday when her rivals ganged up on her and questioned whether her tax-the-rich rhetoric was too “punitive” for an already polarized nation.

The more moderate 2020 Democratic hopefuls took aim at Ms. Warren’s far-left agenda and plans for a wealth tax to finance a host of new benefits from tuition-free college to universal childcare.

“We need to be focused on lifting people up and sometimes I think that Sen. Warren is more focused on being punitive or putting some part of the country against the other,” said former Rep. Beto O’Rourke of Texas.

Ms. Warren was baffled by his charge. “I am shocked at the notion that anyone thinks I am punitive,” she said.

The aggressive challenges to the Massachusetts senator, coupled with deferential treatment of former Vice President Joseph R. Biden, underscored Ms. Warren’s new status as the leader in the race.

In going after Ms. Warren, the Democrats clashed on familiar ground during the party’s fourth primary debate, including how far to go toward a government-run “Medicare for All” health care system.

Mr. Biden batted away questions about his son Hunter’s sweetheart foreign business deals by saying in the Democratic debate Tuesday that President Trump’s corruption was the real issue.

The other top Democratic presidential hopefuls cooperated, giving Mr. Biden a wide berth to avoid the questions of nepotism and corruption involving Hunter Biden. Instead, they piled on in demonizing Mr. Trump and trying to one-up one another on how strongly they vouched for the constitutional necessity not just to impeach him but also remove him from office.

“This is about Trump’s corruption. That is what we should be focused on,” Mr. Biden said. “What I think is so important is that we speak of how important it is to remove this man from office.”

Sen. Cory A. Booker of New Jersey, who is struggling in the polls, came to Mr. Biden’s defense. He said the only person enjoying watching Mr. Biden answer for his son’s lucrative overseas paydays was Mr. Trump.

“He should not have to defend himself,” said Mr. Booker, appearing as if he was auditioning for a spot on a Biden ticket.

Hunter Biden’s lucrative business deals in Ukraine and China while his father was vice president now dog the elder Mr. Biden’s campaign. His $600,000-a-year job on the board of a Ukrainian natural gas company is also at the center of the House Democrats’ impeachment inquiry. Mr. Trump is accused of abusing his office when he asked the Ukrainian president to investigate the Bidens.

While going after Ms. Warren in the party’s fourth primary debate, the Democratic contenders often clashed on familiar ground, such as how far to go toward a government-run Medicare for All health care system.

South Bend, Indiana, Mayor Pete Buttigieg took Ms. Warren to task over her reluctance to say whether she will raise taxes on the middle class to pay for her Medicare for All vision.

“I have made clear what my principles are here, and that is costs will go up for the wealthy and for big corporations, and for hard-working middle-class families, costs will go down,” Ms. Warren said when asked directly whether her plan would lead to middle-class tax increases.

Mr. Buttigieg frequently took on a more forceful tone, contrasting with past low-key debate performances. He is considered in the best position to the race to emerge as the more moderate alternative to Ms. Warren should Mr. Biden’s campaign collapse.

Turning to Ms. Warren, Mr. Buttigieg said voters are fed up with elected leaders that are unwilling to answer “yes-or-no” questions, pressing her to say whether she’d raise taxes as Sen. Bernard Sanders admits will be necessary for Medicare for All.

“This is why people here in the Midwest are so frustrated with Washington in general and Capitol Hill in particular,” Mr. Buttigieg said to Ms. Warren. “Your signature, senator, is to have a plan for everything — except this.”

Entrepreneur Andrew Yang slammed her proposed wealth tax. He warned that the idea failed when tried in other countries.

“The problem is that it has been tried in Germany, France, Denmark, Sweden and all those countries ended up repealing it because it had massive implementation problems and did not generate the revenue that they projected,” he said. “If we can’t learn from the failed experience of other countries, what can we learn from?”

The candidates found agreement on the impeachment question.

Ms. Warren said House Democrats’ impeachment push wasn’t a distraction from the party’s agenda.

“Sometimes there are issues that are bigger than politics, and I think that is the case with this impeachment inquiry,” she said.

Mr. Sanders agreed and called Mr. Trump the “most corrupt president” in the nation’s history.

“This is a president who is enriching himself while using the Oval Office to do that, and that is outrageous,” Mr. Sanders said.

While popular among Democrats, the impeachment question is not a slam dunk among all Americans.

A Quinnipiac Poll this week showed that 46% of Americans approve of impeachment and removal of Mr. Trump, compared to 48% who say he should not be impeached and removed from office.

Shortly before the candidates joined in an impeachment frenzy on the debate stage, House Speaker Nancy Pelosi announced that the decision to launch an impeachment inquiry would not be put to a vote. The announcement fueled Republican criticism that the inquiry was an unfair partisan exercise.

Mr. Biden and Ms. Warren stood shoulder to shoulder at center stage on the campus of Otterbein University, flanked by 10 of their rivals in the largest primary debate in history.

The showdown was the first to play out since the House launched an official impeachment inquiry, Mr. Sanders of Vermont suffered a heart attack and Ms. Warren emerged as Mr. Biden’s top rival.

Ms. Warren has been on the rise in polls, sprinting past Mr. Biden in Iowa and New Hampshire, the two states that host the opening contests in February.

Mr. Biden has struggled to match the appeal Ms. Warren and Mr. Sanders have with far-left activists, and he has trailed them and Mr. Buttigieg in the latest fundraising reports, fueling more doubt about his staying power and cutting into the initial belief that he is the most electable candidate.

Mr. Biden, meanwhile, has become Mr. Trump’s top target after the bombshell whistleblower complaint accusing the president of using U.S. military assistance to pressure Ukraine’s president to investigate the business dealings of Mr. Biden and his son Hunter. Mr. Trump has spun the accusation into an attack against Mr. Biden, saying the Democrat and his family are the corrupt ones and running with that message in attack ads.

Hunter Biden has tried to stop the bleeding by announcing he is leaving the board of a Chinese private equity company and forgoing all foreign work if his father becomes president. The former vice president says Mr. Trump is afraid of facing him in the general election.

The showdown in the Columbus suburbs was viewed as a make-or-break opportunity for some of the lower-tier candidates. The Democratic National Committee heightened the fundraising and polling thresholds to qualify for the fifth debate in Georgia next month.

As of Tuesday, former Housing and Urban Development Secretary Julian Castro, Rep. Tulsi Gabbard of Hawaii, Sen. Amy Klobuchar of Minnesota and Mr. O’Rourke were in jeopardy of missing the cut.

The DNC is requiring candidates to get at least 5% in at least two approved polls in Iowa, New Hampshire, Nevada and South Carolina or 3% in at least four national or early-state polls.

The decision to hold Tuesday’s debate in the Columbus suburbs fueled speculation over the role Ohio will play in the 2020 election.

Barack Obama carried Ohio in 2008 and 2012, and Mr. Trump carried the state by 8 percentage points in 2016 over Democrat Hillary Clinton.

The Trump campaign, meanwhile, launched a pre-emptive strike against the candidates by flying a 35-by-105-foot banner over the city that read in all capital letters: “Socialism destroys Ohio jobs. Vote Trump.”

“While Democrats will use the debate stage to paint a glamorous view of their socialist agenda, Team Trump is here to expose the truth behind their job-killing policies and remind Ohioans what’s at stake in 2020,” said Tim Murtaugh, Trump campaign spokesman.

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