Democratic presidential candidate Sen. Bernie Sanders (I-Vt.) and Sen. Elizabeth Warren (D-Mass.) embrace after the Democratic presidential debate Tuesday night at the Fox Theatre in Detroit. (Justin Sullivan/Getty Images)

The Democratic presidential debate Tuesday night showcased intense splits between the party’s candidates over Medicare-for-all, as the party’s moderates worked to undermine the liberals’ plan for a national health insurance system.

Sens. Bernie Sanders (I-Vt.) and Elizabeth Warren (Mass.) marshaled arguments in support of a single-payer health system as their debate opponents — including former congressman John Delaney (Md.) and former governor John Hickenlooper (Colo.) — identified new lines of attack and counterarguments.

Here were three of the key Medicare-for-all disputes in the debate and the background behind each:

●Would Medicare-for-all force millions of families off their insurance? Several candidates fought Tuesday over the degree to which Sanders’s plan, backed by Warren, would amount to throwing hundreds of millions of Americans off their current health insurance plan.

About half of the country — more than 150 million people — receives health insurance from their employer. The other half is covered by a public program (such as Medicare for the elderly or Medicaid for the poor and disabled), purchases insurance directly from an insurer or has no insurance.

Sanders’s Medicare-for-all plan would move every American into one government insurer in four years, while providing them with medical, vision, and dental care at no cost.

Advocates for such a plan, sometimes called a single-payer system, believe forcing everyone into the same pool is necessary to restrain U.S. health care costs. In theory, doing so would give the federal government leverage over health-care providers — such as hospitals — to accept lower payment rates. (More on that part of this dispute later.) The United States spends far more than other countries on health care, despite lagging behind on key health indicators such as life expectancy and infant mortality.

But critics have latched onto the potential political ramifications of mandating that millions of people with employer-based care move to a government system. They have pointed to polling suggesting majorities of Americans like their employer-provided insurance, and warn there could be a significant public blowback from such a large federal intervention.

This debate has for months sparked fierce discussions in Democratic policy circles, and did so again Tuesday night.

“We don’t have to go around and be the party of subtraction, and telling half the country, who has private health insurance, that their health insurance is illegal,” Delaney said.

Hickenlooper also argued that Sanders’s plan deprives Americans of freedoms to choose between a government and private plan: “You know, it comes down to that question of Americans being used to being able to make choices, to have the right to make a decision.”

However, Sanders and Warren held their ground. They and their allies have pointed out that millions of families lose their insurance every year if they lose their job or lose eligibility under a public plan for various reasons. One study cited by the left-leaning People’s Policy Project suggested that one in four non-elderly adults are uninsured within a given year, meaning millions of people already cycle in and out of insurance.

Sanders said his plan is best “if you want stability in the health-care system.”

Warren similarly hit back at the accusation: “We should stop using Republican talking points in order to talk with each other about how to best provide that health care.”

● Would Medicare-for-all raise taxes on the middle class? Democratic presidential candidates, including Barack Obama, have traditionally shied away from embracing plans that would raise taxes on the middle class.

Sanders has said that his single-payer plan would raise taxes on the middle class but that amount would be more than offset because people would no longer pay deductibles, co-payments or premiums for health insurance. Sanders has said one option to fund Medicare-for-all would be from a 4 percent tax on employees, exempting families earning less than $29,000.

Warren appeared to join Sanders in making that argument under pressure from CNN’s Jake Tapper to answer whether she supports raising middle-class taxes to pay for the plan.

“Middle-class families are going to pay less out of pocket for their health care,” she said. Pressed again for clarification, she added, in an implicit acknowledgment of potential tax increases: “For middle-class families, costs — total costs — will go down.”

But other candidates have sought to embrace proposals that are less expensive. Former congressman Beto O’Rourke of Texas has backed a “Medicare for America” plan, which would place the uninsured and those who are publicly insured in an expanded government program. Anyone could buy into the program but millions of Americans would not be forced to surrender their employer-sponsored care.

O’Rourke denied his health plan would raise middle-class taxes. The plan O’Rourke supports would raise taxes on income above $500,000, as well as on tobacco, beer, wine, liquor and soft drinks. It would also eliminate the 2017 Republican tax law, which cut some middle-class taxes.

“The middle class will not pay more in taxes in order to ensure that every American is guaranteed world-class health care,” he said, later adding: “I have a better path.”

Pete Buttigieg, the mayor of South Bend, Ind., who has been vague about the details of his plan, sidestepped the question of whether his legislation would increase middle-class taxes. Buttigieg earlier in the campaign said he supports Medicare-for-all, but has since said he supports a public option in which the government would offer a public plan that competes with private insurers, rather than outright replaces them.

“Clearly the candidates did not want the talking point that middle-class taxes would go up,” said Larry Levitt, senior vice president at Kaiser Family Foundation. “Tax increases are a potent line against Medicare-for-all, though it would likely lead to the middle-class paying less for health care overall.”

● Would single-payer devastate rural hospitals? Opponents of Medicare-for-all gave dire warnings about its potential impact on hospitals, arguing they would be at risk of further closures under a government-run system.

One key selling point of Medicare-for-all is that it would allow the United States to lower medical spending by reducing payment rates for hospitals and physicians. But many hospitals barely break even and rely on payments under private insurance — which are higher than those of Medicare — to survive.

At the first debate, Delaney claimed that all hospitals would close under single-payer, a claim dismissed by fact-checkers. But how to prevent hospitals from closing would be a difficult policy challenge under Medicare-for-all, said Harold Pollack, a health-care expert at the University of Chicago, who noted that many rural hospitals survive only because of high private insurance rates.

Last year, a record 46 percent of rural hospitals across America lost money, while more than 400 are at “high risk of imminent failure.”

“It is a very real challenge,” Pollack said. “If we went to a single-payer system, we would have to figure out how to support these institutions another way.”

Delaney pared back his argument Tuesday, but maintained that single-payer would force hospitals “into an underfunded system.”

Sanders responded that hospitals would save significant amounts of money under single-payer because they will no longer have to spend “a fortune doing billing and the other bureaucratic things that they have to do today.” Sanders has also recently proposed a fund that would allow local governments to purchase hospitals in financial distress.