For nearly six years, Speaker Paul D. Ryan has championed the new approach, denounced by Democrats as “voucherizing” Medicare. Representative Tom Price of Georgia, the House Budget Committee chairman and a leading candidate to be Mr. Trump’s secretary of health and human services, has also embraced the idea, known as premium support.
And Democrats are relishing the fight and preparing to defend the program, which was created in 1965 as part of Lyndon B. Johnson’s Great Society. They believe that if Mr. Trump chooses to do battle over Medicare, he would squander political capital, as President George W. Bush did with an effort to add private investment accounts to Social Security after his re-election in 2004.
Democrats will “stand firmly and unified” against Mr. Ryan if he tries to “shatter the sacred guarantee that has protected generations of seniors,” said Representative Nancy Pelosi of California, the Democratic leader.
Republicans have pressed for premium support since Mr. Ryan first included it in a budget blueprint in 2011. As he envisions it, Medicare beneficiaries would buy health insurance from one of a number of competing plans. The traditional fee-for-service Medicare program would compete directly with plans offered by private insurers like Humana, UnitedHealth Group and Blue Cross Blue Shield.
The federal government would contribute the same basic amount toward coverage of each beneficiary in a region. Those who choose more costly options would generally have to pay higher premiums; those who choose plans that cost less than the federal contribution could receive rebates or extra benefits.
Supporters say this approach could save money by stimulating greater price competition among insurers, who would offer plans with lower premiums to attract customers.
Democrats say that premium support would privatize Medicare, replacing the current government guarantee with skimpy vouchers — “coupon care for seniors.” The fear is that the healthiest seniors would choose private insurance, lured by offers of free health club memberships and other wellness programs, leaving traditional Medicare with sicker, more expensive patients and higher premiums.
“Beneficiaries would have to pay much more to stay in traditional fee-for-service Medicare,” said John K. Gorman, a former Medicare official who is now a consultant to many insurers. “Regular Medicare would become the province of affluent beneficiaries who can buy their way out of” private plans.
Republicans say their proposal would apply to future beneficiaries, not to those in or near retirement. But the mere possibility of big changes is causing trepidation among some older Americans.
“I am terrified of vouchers,” said Kim Ebb, 92, who lives in a retirement community in Bethesda, Md., and has diabetes, atrial fibrillation and irritable bowel syndrome. “You get a fixed amount of money to draw on for your expenses. Then you are on your own.”
Charles R. Drapeau, 64, of East Waterboro, Me., said he was rattled by the Republican plans.
“I’m scared to death,” said Mr. Drapeau, who has multiple myeloma, a type of blood cancer, and takes a drug that costs more than $10,000 a month. “We don’t know exactly how it will work, but just the fact that they are talking about messing with Medicare, it’s frightening to me.”
Senator Richard M. Burr, Republican of North Carolina, has proposed a version of premium support, and other Republican senators have expressed interest, but the idea has not gained as much traction in the Senate as in the House.
The impact of premium support on Medicare beneficiaries depends on details of the plan to be specified by Congress. A crucial question is how the federal payment would be set. The effects would almost surely vary from one market to another, depending on whether private plans cost more or less than the traditional fee-for-service Medicare program.
Mr. Gorman said that premium support would be “a seismic change” in Medicare and could increase costs for many people in the traditional fee-for-service program, fueling a big increase in enrollment in private Medicare Advantage plans.
Enrollment in private plans is already on the rise, having increased more than 55 percent since adoption of the Affordable Care Act in 2010.
It is not just Republicans who have expressed interest in the idea. Alice M. Rivlin, who was the director of the White House Office of Management and Budget under President Bill Clinton, told Congress in 2012 that she favored a bipartisan proposal for premium support because health plans and providers would then “seek every possible way to provide higher-quality care at a lower cost.”
The nonpartisan Medicare Payment Advisory Commission, which advises Congress, has explored the idea of premium support and endorsed the principle that Medicare payments should be financially neutral — “that is, equal for fee-for-service and Medicare Advantage in each market.”
The Congressional Budget Office analyzed two of the leading options and found that “most beneficiaries who wished to remain in the fee-for-service program would pay much higher premiums, on average, under either alternative.” At the same time, the budget office said the proposal could slow the growth of Medicare spending if more beneficiaries enrolled in lower-cost private plans.
Nearly a third of the 57 million Medicare beneficiaries are already in private Medicare Advantage plans, and the government pays a monthly rate for each of those beneficiaries.
But, the budget office notes, several features of current law limit the degree of competition among insurers, and the traditional Medicare program does not bid against the private plans.
In a premium support system, each insurer would submit a bid showing the amount of money it was willing to accept to provide care for a typical Medicare beneficiary. Congress would need to define the bid for traditional Medicare. It could, for example, be the expected cost of providing care for a typical beneficiary in the fee-for-service program.
Medicare would pay the same basic amount on behalf of all beneficiaries in a region, regardless of whether they chose a private plan or traditional Medicare.
Nationwide, on average, Medicare spends about 2 percent more for a beneficiary in a private plan than it would for the same person in the fee-for-service program, according to the Medicare Payment Advisory Commission. But in some large urban areas with many competing private plans, those are less expensive than traditional Medicare.
Consumer advocates express several concerns about premium support. Private plans, under pressure to rein in costs, could respond by creating smaller networks of doctors and hospitals. Such plans would then be less attractive to sicker patients who need more health care services.
“What happens if the voucher doesn’t grow with the cost of health care?” asked Leslie B. Fried, a health lawyer at the National Council on Aging, a service and advocacy group. “Will people have more and more out-of-pocket costs?”
Ms. Fried said that having a healthy fee-for-service Medicare program was important not just for the 38 million people who have such coverage but also for people with private plans. Sometimes, she said, people switch from private plans to traditional Medicare when they develop serious illnesses and want a broader array of doctors.
For their part, insurers say the government would have an unfair advantage in any system of premium support because it would be regulating health plans and competing with them at the same time. Medicare officials set detailed standards for private plans and can fine them or suspend their marketing and enrollment activities if they violate the rules.