Yet since the Supreme Court upheld the Democrats’ 2010 health care law, Republicans, led by Mitt Romney, have reversed tactics and attacked the president and Democrats in Congress by saying that Medicare will be cut too much as part of that law. Republicans plan to hold another vote to repeal the law in the House next week, though any such measure would die in the Democratic-controlled Senate. “Obamacare cuts Medicare — cuts Medicare — by approximately $500 billion,” Mr. Romney has told audiences. That is a reprise of Republicans’ mantra of the 2010 midterm elections, which gave them big gains at both the state and federal levels and a majority in the House. Yet the message conflicts not only with their past complaint that Democrats opposed reining in Medicare spending, but also with the fact that House Republicans have voted twice since 2010 for the same 10-year, $500 billion savings in supporting Mr. Ryan’s annual budgets. The result is a messaging mess, even by the standards of each party’s usual election-year attacks that the other is being insufficiently supportive of older people’s benefits. And in this year’s contests, which both parties describe as a referendum on who can best correct the nation’s economic course, such talk underscores how far Republicans and Democrats are from truly squaring with the public about curbing the growth of the major entitlement programs: Medicare, Medicaid and, to a lesser extent, Social Security. That growth is driving the projections of a federal debt that is mounting unsustainably as the population ages and health care costs rise. “A pox on both their houses,” said Ron Haskins, a former Congressional staff member who is now a scholar of social programs and budgeting at the Brookings Institution. Democrats and Republicans “know they have to do something about Medicare, and then they harass each other about cutting Medicare. It’s so discouraging to me, but I’m a Republican, so I’m much more distraught about Republicans.” And, Mr. Haskins added, “$500 billion is modest compared to what Ryan would do.” Under Mr. Ryan’s budget, which Mr. Romney has supported but which has been blocked each year in the Senate, Medicare would not pay for the medical fees of future beneficiaries, as it currently does. Instead it would provide “premium support,” limited payments — vouchers, Democrats say — that beneficiaries could use to buy insurance policies in the private sector. And Medicaid, which increasingly goes toward nursing home care for older people, would become a capped block grant to states, forcing them to make significant cuts. In their attacks, Republicans have said in speeches and in television advertisements that the Democrats’ projected $500 billion in Medicare savings will “strip,” “gut,” “rob” or “raid” older people’s benefits. “Ron Barber will hurt Arizona seniors,” said an ad this spring from the House Republicans’ campaign committee in support of the Republican who ultimately lost to Mr. Barber, a Democrat, in a special election to replace Representative Gabrielle Giffords. Objecting to such attacks, Representative Chris Van Hollen of Maryland, the senior Democrat on the House Budget Committee, said in an interview: “There are two issues here: One, there were no cuts to Medicare benefits. And in fact, benefits were strengthened.” Independent fact-checking groups have repeatedly knocked down the Republicans’ claims. “A discredited claim is making a comeback following the U.S. Supreme Court ruling upholding most of the national health care reform law,” PolitiFact recently wrote in one such analysis. Republicans stand by their attack. They say the problem with the Democratic approach is that the reductions do little to bolster Medicare’s stability, with the money diverted to initiatives in the health care law. “Democrats are still the only party in Washington to cut $500 billion from Medicare in order to help pay for Obamacare,” said Paul Lindsay, spokesman for the National Republican Congressional Committee. “It’s a fact that did not go unnoticed among seniors in 2010, and one that we will continue holding Democrats accountable for in our ads this fall.” But the $500 billion in reductions would come through cuts in the projected growth of Medicare and would mainly affect hospitals and other providers of medical care, some of whom supported the health care measure nonetheless because it would extend coverage to up to 30 million uninsured Americans, raising the number of paying customers. Other savings would result from lower subsidies for private insurers selling Medicare Advantage plans, which offer older people extra features like vision care and gym memberships. The insurers could not cut basic Medicare benefits. Democrats used the projected $500 billion in savings to help pay for expanding older people’s benefits. The health care law says that some preventive care services like mammograms must be free to patients, and it closed the “doughnut hole” in the Medicare prescription drug program, which had left many older people paying full price for prescriptions above a certain level. While Republicans have backed the spending reductions, even as they have attacked Mr. Obama and the Democrats for enacting them, they would end the new benefits. Mr. Ryan, of Wisconsin, was unavailable for comment, but, pressed on the issue on ABC’s “This Week” on Sunday, he said: “Well, our budget keeps that money for Medicare to extend its solvency. What Obamacare does is it takes that money from Medicare to spend on Obamacare.” Robert Greenstein, the executive director of the left-leaning Center on Budget and Policy Priorities, called Mr. Ryan’s claim “somewhere between a misstatement and a flat-out untruth.” Mr. Greenstein, among others, said that Democrats were not double-counting the $500 billion in savings — by claiming that it both improves Medicare’s financial outlook and helps finance new benefits — any more than were the Republicans, who say they would use the savings both to shore up the Medicare trust funds and to reduce the federal debt. The Congressional Budget Office and the chief actuary for the Medicare and Medicaid programs, Richard S. Foster, have concluded that the $500 billion in savings would extend the solvency of Medicare’s hospital insurance trust fund. Since the passage of the health care law, known as the Affordable Care Act, the Medicare trustees have shifted the projected date of insolvency to 2024 from 2016. Mr. Foster, in this year’s report by the trustees, wrote that “the Affordable Care Act makes important changes to the Medicare program and substantially improves its financial outlook.”