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Democratic presidential candidates tangled on health care in their first debate Wednesday, agreeing on the need for universal coverage but disagreeing about whether private insurance should be maintained.

The 10 candidates on the stage in Miami Wednesday were asked who would abolish private insurance, and only Massachusetts Senator Elizabeth Warren and New York Mayor Bill de Blasio raised their hands. Warren supports a “Medicare for all,” government-run system.

Warren said insurance companies try to raise as much as they can in premiums while not making payments and “Medicare for all solves that problem.”

Former Texas Representative Beto O’Rourke said he doesn’t support abolishing private insurance, causing de Blasio to interject: “Hey, wait, wait, Congressman O’Rourke, Congressman O’Rourke, private insurance is not working for tens of millions of Americans. Why are you defending private insurance to begin with?”

It was the first time the candidates disagreed in a debate that started with general agreement on the need for the U.S. economy to do more to help those who aren’t wealthy and gave lower-polling candidates such as de Blasio and former Representative John Delaney a change to emerge.

Private insurance

Delaney got big applause when he questioned why the candidates would take away private employer insurance, when it’s working. Senator Amy Klobuchar also said she doesn’t support undermining the private insurance—and tried, without success, to join the debate while moderators regularly called on Warren.

Warren started the first debate among Democratic presidential candidates with a robust defense of her plans for “structural” change to the U.S. economy, saying the current system is tilted far too much to benefit the wealthy.

“When you’ve got a government, when you’ve got an economy, that does great for those with money and isn’t doing great for everyone else, that is corruption pure and simple,” Warren said. “We need to call it out, we need to attack it head on and we need to make structural change in our government, in our economy and in our country.”

The economy, taxes, income inequality and the question of breaking up big companies dominated the opening rounds of the first debate among the Democrats seeking to challenge President Donald Trump Wednesday night in Miami.

Comparisons

Twenty Democrats will give voters the first side-by-side comparison of their plans and styles in two nights of debates that will serve as the first stage of winnowing for a historically large field of candidates.

The nationally televised debates in Miami is splitting the candidates into groups of 10 on Wednesday and Thursday, with each face-off including a mix of top-tier and lower-polling contenders. Warren is the highest-polling candidate on Wednesday night, trailing front-runner Joe Biden, the former vice president, and Senator Bernie Sanders, who appear on Thursday.

It will be the first time so many of the Democratic hopefuls will appear together on the same stages after months of individual town halls and events in early primary and caucus states. With so many of the candidates largely aligned on the big issues, the debates provide an opportunity to set themselves apart, especially for those at the back of the pack.

At least a dozen debates are scheduled. A slip by one of the front-runners or a breakout performance by one of the lower-polling contenders has the potential to shake up the race, which has been dominated by Biden, Sanders, Warren, Senator Kamala Harris and South Bend, Indiana, Mayor Pete Buttigieg.

Howard Dean, a former Democratic National Committee chairman and candidate for the party nomination, said he expects the field of 24 candidates will eventually be cut to 10 candidates before the first nominating contest, the Iowa caucuses in February.

RELATED: Issues that divide 2020 Democrats

Donna Brazile, another former DNC chairwoman who appeared with Dean at a Washington Post forum on Wednesday, agreed that no more than half of the current candidates will remain in the race by early next year. She said the first rounds of debates will give lower-tier candidates enough exposure to determine in a matter of months whether they can raise enough money and gain a big enough following to sustain their campaigns.

“We’ll be down to a rational number by Easter,” Brazile said.

The candidates aren’t being given much time to make their cases in the first debates. There are no opening statements, and they’ll be allotted 60 seconds to answer questions and 30 seconds to respond to any follow-ups.

The debates come at a fraught time internationally and domestically. There are heightened tensions between the U.S. and Iran after an unmanned American drone was shot down, and Trump is engaged in a trade war with China while fighting with Democrats on immigration amid a humanitarian crisis on the southern border.

Warren, Harris and Minnesota Senator Amy Klobuchar are among the Democratic candidates who visited a detention center in Florida this week to highlight the wrenching conditions for migrants, including children, as Congress debates different versions of an aid bill that must be reconciled.

The party is also divided about whether to pursue impeachment proceedings against Trump, with Special Counsel Robert Mueller set to testify before Congress on July 17. While many in the field have called for it, House Speaker Nancy Pelosi has resisted without an “ironclad” case and out of concerns about bolstering Trump’s re-election.

Warren is sharing the Wednesday stage with former Texas Representative Beto O’Rourke and Senator Cory Booker of New Jersey, who are polling behind the top five, as well as seven candidates who are generating less that 3% in most polls: Klobuchar, former Housing and Urban Development Secretary Julian Castro, Representatives Tulsi Gabbard and Tim Ryan, New York City Mayor Bill de Blasio, Washington Governor Jay Inslee and former Representative John Delaney.

The Massachusetts senator has steadily risen in polls over the last two months and distinguished herself in the crowded field so far with a breadth of policy positions. They include a proposed annual tax on households with a net worth of more than $50 million and a 7% tax on company profits of more than $100 million.

Warren has been focused on claiming the mantle of leader of the party’s progressive faction, and she contrasts her plans with the more incremental approach of Biden, who is focusing his campaign almost entirely on Trump.

Biden and Sanders will join rivals including Harris and Buttigieg in Thursday night’s debate.

Three candidates did not qualify for the debates: Montana Governor Steve Bullock, Mayor Wayne Messam of Miramar, Florida, and Massachusetts Representative Seth Moulton. Bullock’s campaign says he has already met the qualifications to be on stage for the second round of debates, set for Detroit on July 30 and 31 and hosted by CNN.