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.