(CNN) Americans generally don't like the idea of giving up their private health insurance. Hospitals and doctors don't want them to, either.

Private insurers typically pay medical providers a whole lot more than Medicare and Medicaid. And that's one of the main reasons why many hospitals and doctors oppose Medicare for all proposals that would eliminate or minimize private insurance.

The renewed interest in Medicare for all has prompted the American Hospital Association, Federation of American Hospitals and American Medical Association to join a national coalition seeking to chill the growing fervor. Instead, they are pushing to strengthen employer-based policies, which currently cover roughly half of Americans.

It's not hard to see why.

Medicare payments only covered 87% of costs in 2016, the most recent data available from the American Hospital Association. But private insurers paid nearly 145% of their policyholders' hospital expenses.

"Hospitals are already paid far less than the cost of caring for Medicare patients, and more patients with Medicare would strain hospitals even more, and could threaten hospitals' survival," wrote Rick Pollack, chief executive of the association, in a blog post last month.

Private insurance payments provide the funding hospitals need to offer the care that Americans expect, said Chip Kahn, chief executive of the Federation of American Hospitals, which represents for-profit institutions.

"It would be great if we had this national health insurance, but the question is would you then have the system to provide the services," Kahn said.

The main Medicare for all legislation would let either the federal government or regional directors set reimbursement rates and create annual budgets based on the Medicare system.

Vermont Independent Sen. Bernie Sanders' Medicare for all bill, which he floated in 2017 and expects to reintroduce soon, calls for continuing Medicare's current payment formulas but doesn't establish the rates. The House version, unveiled in late February by Democratic Rep. Pramila Jayapal of Washington, would establish an annual lump-sum budget for hospitals and other institutions, but pay doctors based on the services they provide.

While the key industry group for doctors opposes single-payer proposals such as Medicare for all, some physicians are more open to it, particularly younger ones.

Under Medicare for all, there would likely be some redistribution, acknowledged a Sanders staffer. Hospitals and doctors that see a lot of privately insured patients could see their reimbursements drop, but those that take care of the uninsured and Americans on Medicaid, which covers the poor, could wind up making more money under Medicare for all than they do now.

"There are tradeoffs," said Sanders spokesman Josh Miller Lewis. "Our goal is to ensure every single person is guaranteed health care, and we do it in the most cost-effective way."

But Medicare pays hospitals about 40% less than private insurance for inpatient services and doctors about 30% less for their treatment, according to Charles Blahous, a senior research strategist at the conservative Mercatus Center at George Mason University and a former trustee for Social Security and Medicare. And the gap is expected to grow over time, he says, citing data from the Centers for Medicare and Medicaid Services' Medicare actuary.

Other studies of the Sanders plan assume that Medicare will increase its rates to keep up with or even slightly exceed costs -- though that would levy a heavier burden on taxpayers.

Plus, proponents say, medical providers will be able to shrink administrative costs, which will save them money, and they will benefit from everyone having coverage.

"The vast majority of doctors will not get paid less," Jayapal told reporters before unveiling her bill. "In fact, they'll be seeing many more clients and they won't have to spend sometimes up to 25% of their time on administrative stuff."

To contain health care costs, Jayapal wants to pay hospitals under a so-called global budget system, which other developed countries use.

So does Maryland, which has specified the amount of annual revenue hospitals can receive from Medicare, Medicaid and private insurers since 2014.

An analysis by research group RTI International in 2017 found that hospitals adjusted their rates to remain within their budgets, but that didn't hurt them financially. Also, hospitals reduced spending on their emergency departments and some other outpatient services and saw admissions decline. They also curtailed unnecessary care among Medicare beneficiaries.

Yet some experts question whether Maryland's system can be replicated nationally, especially because Medicare pays higher rates in the state.

Also, since consumers would pay virtually nothing under Sanders' and Jayapal's plans, more people would seek care.

"It would cause health care spending to balloon beyond what would be affordable for the budget," said Eric Roberts, assistant professor of health policy at the University of Pittsburgh. That could then lead to rate cuts or service reductions, both of which are tough to implement. "You get yourself potentially into a fiscally unsustainable scenario."