They can't both be right, and no matter which side is, this is one campaign clash with consequences extending well beyond Nov. 6.
Mitt Romney "would replace guaranteed benefits with a voucher system," says a commercial that President Barack Obama's campaign aired in several states this fall. "Seniors could pay $6,000 more a year. A plan AARP says would undermine Medicare," it adds, making claims that Democrats in congressional campaigns echo in ads of their own from New York to California.
Not surprisingly, Republican presidential nominee Romney describes the issue differently as he describes what he and running mate Paul Ryan want to do.
"You pay into Medicare for years. Every paycheck. Now when you need it, Obama has cut $716 billion from Medicare. Why? To pay for Obamacare," one of Romney's ads says. "The Romney/Ryan plan protects Medicare benefits for today's seniors and strengthens the plan for the next generation," it says, a pitch that party strategists say is helping Republicans up and down the ballot blunt a perennial Democratic campaign attack.
Given the millions of dollars both sides are spending, the winner of the presidential election may well be able to claim a Medicare mandate. Add the near certainty that deficit reduction will be prominent on the 2013 agenda. Then factor in the official estimate that the Medicare fund that pays for inpatient care will run out of money in a little more than a decade.
The result is a near-certainty that significant change is coming for a program that provides health care to 49 million beneficiaries, the large majority of them age 65 and older.
Like so much else in a gridlocked capital in the throes of a tight election, much depends on where the argument begins.
A polling advantage on Medicare for Obama and fellow Democrats isn't surprising because surveys for decades have shown the public favors them on the issue. But a narrowing GOP deficit would be, and that's what Republicans say is happening, citing surveys in previous years that showed a Democratic advantage on Medicare of 20 points.
The polls vary. A Washington Post-ABC survey this month showed Obama with a 54-41 advantage over Romney on Medicare among likely voters, while a Pew survey made it 46-43 for Obama.
"The Romney/Ryan Medicare message has neutralized the issue," GOP pollster David Winston wrote in a memo for the American Action Network in August, shortly after Ryan, a Wisconsin congressman, was placed on the Republican ticket.
He and others say the passage of Obama's health care plan has given Republicans a new argument to make - that passage of the legislation involved cutting $716 billion from Medicare over a decade. It's a point that independent voters dislike about the president more than anything else, according to Charlie Black, a Republican strategist and informal adviser to Romney.
But Mark Mellman, a Democratic pollster, said, "Nobody would put up all these ads if we didn't believe it was working."
Rep. Steve Israel of New York, head of the Democratic Congressional Campaign Committee, says he has a two-word answer to the GOP claims: Ron Barber. An Arizona Democrat, Barber won a special election in June to replace Democratic Rep. Gabrielle Giffords, who had been wounded in an assassination attempt. Both parties test-marketed ads on Medicare and Obama's health law in anticipation of the fall campaign.
The dispute over the ads themselves is no less intense.
Democrats reject the claim they cut Medicare to help finance the health law.
They say that law was financed partially by reducing the projected growth of Medicare, not cutting it. Ironically, it is the same argument that Republicans often fall back on when they are accused of seeking cuts to education or other programs.
Democrats also say that none of the $716 billion came from cuts in guaranteed benefits, but primarily from reductions in projected payments to private insurers in the Medicare Advantage program, as well as reimbursements to hospitals and other providers.
They also note that the health law eliminated the doughnut hole, a gap in coverage that required seniors with especially high prescription drug costs to pay large sums out of pocket.
But Republicans accuse Obama and the Democrats of making false accusations of their own.
They stress that neither Romney nor Ryan has proposed any changes for current beneficiaries or those within 10 years of enrolling in Medicare. They also cite independent fact checks concluding that Democratic claims of a $6,400 increase in out-of-pocket costs for seniors under the GOP approach are bogus, based on an outdated version of Ryan's plan.
Republicans also say that unlike Ryan's plan, Romney's does not include a mandatory cap on growth of the overall program to guarantee budget savings. Romney has yet to release details of his own proposal, or even a comprehensive description of ways in which it differs from his running mate's blueprint.
There's no doubt about the millions going into the campaign debate on the issue.
Obama's campaign seized on Medicare shortly after Romney named Ryan as his running mate. It spent nearly $16 million on ads in eight battleground states for several weeks beginning in mid-August, according to records compiled by ad checkers. Romney spent about $7.7 million over roughly the same time period.
There the issue sat, until Romney's strong showing in the first debate on Oct. 3 and Obama's poor one.
Suddenly, the president's campaign was back on the air attacking Romney over Medicare again, trying to blunt the Republican's gains in the polls.
Last week, Romney, too, mentioned Medicare in an ad that begins by cataloging the high unemployment and large deficits during Obama's term. "He just hasn't been able to put in place reforms for Medicare and Social Security to preserve them," the commercial says.
A similar clash is playing out more than two dozen Senate and House races, largely along the same rhetorical lines.
In California, Democratic challenger Raul Ruiz and the party's campaign committee have both paid for ads targeting Rep. Mary Bono Mack's record on Medicare. One accused her of "voting to end Medicare, leaving seniors at the mercy of insurance companies, paying $6,400 more."
The sixth-term congressman aired an ad of her own, and the National Republican Campaign Committee defended her as well.
"The truth: Mary voted to protect Social Security and Medicare. She always will," the congresswoman's ad said, before going on to accuse House Democratic leader Nancy Pelosi of being behind the ads. It claimed the ads were part of a campaign to put liberals back in charge of the House. "We get more taxes, higher spending, fewer jobs."
(Copyright 2012 by The Associated Press. All Rights Reserved.)