WASHINGTON — A little more than two weeks before Election Day, Republicans and Democrats alike say Medicare is working to their political advantage in campaigns for the White House and Congress.

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 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 says 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 surprising, and that’s what Republicans say is happening, citing surveys in previous years that showed a Democratic advantage on Medicare of 20 points.

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.