Medicare is actually three programs:
Part A, hospital insurance, paid for by a 1.45 percent payroll tax.
Parts B and D, insurance for physician services and drug coverage. Taxpayers pay some of the costs, along with income-based premiums paid by seniors.
Medicare Part C is also known as Medicare Advantage. Enrollees in that program divert some of the premiums and taxpayer support into private insurance plans that provide more benefits at an additional cost.
There are co-pays and deductibles for Medicare patients, and some caps on payments.
Because they're partially supported by premiums, Medicare Parts B and D can't go broke. Instead, premiums are increased to cover growing costs for drugs and doctor visits.
Taxpayer subsidies for Medicare Advantage can be reduced -- it's the source of some of the controversial $716 billion, 10-year spending cut in the Affordable Care Act.
Republicans call those reductions a "cut" in Medicare, while Democrats contend they only reduce subsidies for insurance companies offering Medicare Advantage policies. Basic Medicare, they maintain, isn't affected.
Without changes, Part A will exhaust its reserves in 2024. Claims would still be paid, but not at 100 percent. The Kaiser Family Foundation predicts Part A will be "insolvent" in 2016 if the Affordable Care Act is repealed.
In general, Republican plans to shore up Medicare include a quick disclaimer: Persons over age 55 could keep Medicare's taxpayer-supported, fee-for-service program.
"My plan presents no change," GOP nominee Mitt Romney said in August, writing the words on a whiteboard for emphasis.
For those under age 55, most Republicans now back what they call a "premium support plan" for Medicare. Instead of Medicare, seniors would be given a fixed amount of money annually, based on income, that they could use to buy health coverage from private insurers or from Medicare itself.
The goal: To allow private companies to compete for seniors' insurance payments, bringing free-market efficiency to both insurance companies and health care providers in hospitals and clinics.
Private insurance would give seniors more security, more access and allow them to keep insurance coverage they used while working, said Bob Moffit, a health expert at the conservative Heritage Foundation.
"Competition does in fact control costs," Moffit said.
But Democrats, and some elderly advocacy groups, argue that premium support would cost seniors thousands of dollars. The federal payments, they said, would not provide enough cash to buy relatively comprehensive coverage, leaving seniors to either make up the difference out of their own pockets or forgo treatment -- or both.
"A voucher plan would absolutely reduce federal health care spending," said Michael Linden, budget expert at the Center for American Progress. "Would it provide the same health care to senior citizens that they get now? Probably not."
Others worry insurance companies would squeeze providers to lower their costs, yielding lower quality health care.
"Why add another layer of profit?" asked 93-year old Jim Belwood of Overland Park. "I'm not of the strong philosophy that everything is done better in the profit system."
Republicans also promise to repeal the Affordable Care Act, which they call "Obamacare."
Repeal would return $716 billion to Medicare Advantage, but it also would eliminate the health care reform law's Medicare tax increase on high-income wage earners. That would reduce projected income for Part A, potentially hastening its financial problems.
Democrats have been very vocal in what they oppose, but less clear on what they support.
Some, including Missouri Sen. Claire McCaskill, for example, have suggested cutting Medicare's drug and insurance benefits for higher-income individuals, a proposal some Medicare advocates believe would turn the program into income-based welfare, not an entitlement.
And there's no clear indication such limits would provide enough money to close Medicare's funding gap. So to provide additional money, some Democrats promote higher Medicare taxes on the wealthy.
Others suggest higher taxes on fattening food and beverages, and using the cash to help prevent diseases that drive up health care spending.
"Don't voucherize Medicare. Don't cut benefits," said David Kingsley, a statistics professor at the University of Kansas Medical Center and a member of the Gray Panthers, a lobbying group for seniors. "The people who are responsible need to pay. If you go buy a Wendy's burger, then you're going to pay a tax."
Other Democrats and Medicare groups note that a special review board embedded in the Affordable Care Act will be able to limit payments for procedures and medicines, reducing Medicare outlays and thus saving the system.
Republicans call the board a "death panel," which will cut costs by denying the full range of health care options to Medicare patients.
Paths to compromise
Most experts said bridging the gap between a more-private Medicare and the program as it now exists will be extraordinarily difficult.
But a compromise might involve higher Medicare taxes, and fewer Medicare benefits for wealthy seniors, coupled with some expanded options for private insurance under Medicare, phased in, for younger workers.
Other solutions could include required negotiations with drug companies and providers for lower prices, and some version of Kingsley's "sin" taxes.
Government already is involved in setting prices for health care services, and that's likely to continue.
Both sides do agree on this: the Medicare problem isn't really about Medicare.
The program's problems are a symptom of exploding health care costs generally. Those costs must be reduced, either by more direct government intervention, free market forces, or more self-imposed industry efficiency.
Medicare advocates said the Affordable Care Act will reduce costs and should be given time to work. But in a burst of candor, Linden said he didn't really know what would lower health expenses.
"Anybody who says I have the key -- it's the market, it's this or that -- is just not telling the truth," he insisted. "We don't know for sure what's going to bring down health care costs."