To Mr. Obama’s credit, his plan has more teeth than Mr. Ryan’s; if his Independent Payment Advisory Board comes up with savings, Congress must accept either them or vote for an equivalent package. The problem is, the advisory board can’t propose reducing benefits (a k a rationing) or raising fees (another form of rationing), without which the spending target looms impossibly large.

That’s the view of the bipartisan Medicare trustees, whose 2012 report stated: “Actual future Medicare expenditures are likely to exceed the intermediate projections shown in this report, possibly by quite large amounts.”

To be sure, health care cost increases have moderated, in part because of the recession and in part because Medicare has been tightening its reimbursements. But those thumbscrews can’t be tightened forever; Medicare reimbursement rates are already well below those of private providers.

Let’s not forget that with the elderly population growing rapidly, even if cost increases for each beneficiary can be contained, Medicare would still claim a rising share of the American economy.

Medicare needs to take a cue from Willie Sutton, who reportedly said he robbed banks because that’s where the money was. The big money in Medicare is not to be found in Mr. Ryan’s competition or Mr. Obama’s innovation, but in reducing the cost of treating people in the last year of life, which consumes more than a quarter of the program’s budget.

No one wants to lose an aging parent. And with price out of the equation, it’s natural for patients and their families to try every treatment, regardless of expense or efficacy. But that imposes an enormous societal cost that few other nations have been willing to bear. Many countries whose health care systems are regularly extolled — including Canada, Australia and New Zealand — have systems for rationing care.

Take Britain, which provides universal coverage with spending at proportionately almost half of American levels. Its National Institute for Health and Clinical Excellence uses a complex quality-adjusted life year system to put an explicit value (up to about $48,000 per year) on a treatment’s ability to extend life.

At the least, the Independent Payment Advisory Board should be allowed to offer changes in services and costs. We may shrink from such stomach-wrenching choices, but they are inescapable.