Most premium support approaches would retain traditional Medicare, though its fate would be uncertain, a source of controversy. “A lot rides on how the government’s support level differentially impacts the cost to beneficiaries of private plans versus traditional Medicare,” said Timothy McBride, a health economist with Washington University in St. Louis. Geography also plays a role. “If traditional Medicare is disadvantaged, that would hit rural beneficiaries harder, because a larger share of rural America relies on the traditional program than do urban Americans.”

As a report this month from the Congressional Budget Office reveals, how much premium support could save the government varies considerably depending on how stipend levels are established. Across the variations the C.B.O. examined, Medicare spending could fall by as much as 9 percent or as little as about 0.5 percent. But premiums could rise, including the premium for traditional Medicare. Under one projection, the C.B.O. estimates, traditional Medicare’s premium could double.

In all the scenarios the C.B.O. analyzed, stipend levels would be based on bids from Medicare Advantage plans and traditional Medicare that reflect the cost to cover a person for standard Medicare services. Stipend levels would keep pace with overall health care costs, but they could still be lower than what many Medicare beneficiaries receive today.

For example, tying the stipend to the second-lowest bid and requiring all Medicare beneficiaries to be subject to that new, lower level would save $419 billion over 2022-2026, the C.B.O. estimated.

Tying it to the average bid or requiring only new beneficiaries to be subject to the new stipend would save less. In either case, people would have access to plans that don’t cost more than today’s. But those who opted for more expensive plans because they offer more benefits, or the traditional program because it covers any doctor willing to accept Medicare patients, would pay more out of pocket. Consequently, more people would opt for cheaper, private plans — and fewer would choose traditional Medicare.

This worries some health policy experts. “Traditional Medicare has been the leader in reforming the health care payment and delivery system to improve efficiency,” said Paul Van de Water, senior fellow with the Center on Budget and Policy Priorities. “It has outperformed private insurance in holding down the growth of health costs, but its ability to continue to do that would shrink significantly if premium support caused its enrollment to dwindle.”

Exactly how much more people would pay depends not only on the plans they select, but also on where they live. In some markets, many plans, including the traditional program, might charge premiums close to the second-lowest bid. In others, plans that many beneficiaries may want might cost a lot more.

In the premium support debate, there’s a fundamental lesson: It’s conceptually simple to reduce federal spending on health care, but it’s very hard to do so in a way that doesn’t increase costs for at least some consumers. To actually reduce total (not just federal) health care spending for everyone, one has to overhaul how care is delivered, not just how it is paid for. That’s much harder.