Bernie Sanders and Hillary Clinton debate at the University of New Hampshire on Thursday. (AP/David Goldman)

Health care has been the first item on the agenda for Hillary Clinton and Sen. Bernie Sanders in both Democratic presidential debates Thursday and last week. It's one of few issues on which the two candidates have a real difference of opinion -- who should be covered, what kind of coverage they should receive and who should pay the bill.

Both candidates like President Obama's health-reform legislation, the Affordable Care Act. Both talk tough about reducing medical costs and price-gouging by pharmaceutical firms.

But there is disagreement: Sanders's plan would replace much of the existing private insurance industry. In its place, the federal government would collect premiums from Americans and reimburse doctors and hospitals for their services, just as Medicare does now for retirees. He calls his plan "Medicare for All." Clinton, however, supports maintaining the existing system under the Affordable Care Act, also known as Obamacare.

But in the debates Clinton and Sanders haven't fully explored the holes in each other's positions. On Thursday, Clinton said that Sanders wants to "start all over again" on the issue of health care, wrongly implying that if  the senator from Vermont became president, people who have gained coverage under Obamacare would risk losing it. Yet when Clinton has brought up legitimate questions about the cost of Sanders's plan, he hasn't really engaged with them.

In truth, a more straightforward discussion of American health care's deep-rooted problems might make both of them look vulnerable on the issue. Here's a closer look at what Clinton and Sanders really think about health care, why they see things the way they do, and why they aren't talking about the important questions that have been raised about their rhetoric.

What Clinton doesn't want to talk about

Sanders argues for establishing a national, single-payer system to replace the labyrinth of private plans, federal insurance, online marketplaces and government subsidies that Obamacare established. Other countries, he points out, have found ways of making health care accessible to all their citizens, while spending much less per person than does the United States.

"We can guarantee health care to all people in a much more cost effective way," Sanders said Thursday. "In my view, health care is a right of all people, not a privilege, and I will fight for that."

It's basically true that health care is cheaper in other countries. There's reason to believe it's better, too. The United States is unique among the world's developed nations in that we spend buckets of money on medical treatment, but we live relatively short lives.

One reason that health care is so cheap elsewhere is that many countries have a system like the one Sanders is proposing. The advantage of a singer-payer system is that the government is able to negotiate better prices with hospitals and pharmaceutical companies than private insurers can. Under that system, if providers want to walk away from the negotiating table, they'd be giving up a whole lot of customers.

Obamacare does include provisions designed to reduce costs. A body called the Independent Payment Advisory Board is supposed to make recommendations to limit spending on Medicare. Yet some experts are skeptical that Obamacare will be able to meaningfully control costs. The law does not replace the private insurance industry with a single payer, allowing the bargaining power that comes from insuring all patients across the country to remain fragmented.

"It's very important that we try as best we can to wring as much inefficiency out of the health-care system as possible, and it may turn out to be the case that it's just very difficult to do that with the Obamacare setup," Lane Kenworthy, a scholar at the University of California, San Diego, said in an interview last month.

What Sanders doesn't want to talk about

This case for single-payer is strong. To challenge it, Clinton has accused Sanders of misleading voters about the cost of his plan.

"The numbers don’t add up, and that’s a promise that cannot be kept," the former secretary of state said in Thursday's debate. "We should level with the American people."

"That's completely inaccurate," Sanders rejoined. "I don't know what economists Secretary Clinton is talking to."

Then he simply doubled down on a line that Clinton had said was misleading: Sanders claims that under his plan, a typical household would pay just $500 in additional taxes a year, but would save $5,000 in annual health-care costs.

Unfortunately for Sanders, Clinton has a point, according to Kenneth Thorpe, a health expert at Emory University who helped design a single-payer proposal in Sanders's home state of Vermont. In an analysis distributed to reporters last month, Thorpe wrote that Sanders is short about $1.1 trillion a year.

"It’s just not even close to the actual number that would be required to do what he wants to do, which is a laudable thing," Thorpe said.

If single-payer is so cheap in other countries, as Sanders said, then why can't he make the numbers work out? Thorpe argues that Sanders has the same problem that ultimately prevented Vermont from enacting a single-payer plan.

In principle, Thorpe assumes that a single-payer plan could be less expensive on net. In his analysis, he assumed that the federal government as a single payer could save about a quarter of what Americans currently spend on private insurance. Those savings would result from bargaining with drug makers and hospitals while simplifying administrative procedures and reducing overhead.

Sanders's plan, though, would also make the American health-care system much more generous than it is now -- and thus more expensive.

For example, while Medicare requires the elderly to pay deductibles and coinsurance, those would be eliminated in his version of Medicare for All. Instead, the government would pay for everything.  Americans wouldn't pay anything out of pocket besides a premium. That would make the system much more expensive for Uncle Sam.

Also, as Sanders is fond of pointing out during debates, almost 12 percent of Americans are still uninsured. Covering all of them would be costly, as well. Accounting for the taxes that would be necessary to pay for it all, Thorpe estimates that a large majority of households -- about 71 percent -- would be worse off financially under Sanders's plan.

"The disruption and the massive redistribution of who wins and who loses under a proposal like this are just so enormous," said Thorpe, who served in the Bill Clinton administration supervising financial estimates for health-care proposals.

Without the promise of eliminating deductibles and copays, though, the plan would have no appeal politically. Thorpe pointed out that while people might not like their insurance company, under Sanders's proposal, they'd have to give up the plan they have for a government plan that would still require them to pay deductibles and copays out of pocket. And expanding coverage to the Americans who don't have it now would still require Americans to pay more in taxes.

Thorpe agrees with Clinton that the best approach is to try to reduce costs through Obamacare's existing mechanisms.