A HEALTHY SKEPTICISM is always in order with regard to grand political speeches, and House Majority Leader Eric Cantor’s effort Tuesday to reposition and rebrand his Republican Party was no exception. In promising to move from partisan budgetary trench warfare to an agenda both more open to compromise and more clearly connected to the “real-life concerns” of Americans, Mr. Cantor was transparently trying to dig out of the political hole in which his party finds itself. We’ll find out soon enough whether his words really do mark the beginning of a new, more functional era on Capitol Hill.

But there are reasons not to dismiss the speech out of hand. First, it would be strange to condemn Mr. Cantor — or any other politician — for changing his tone, or his policy, out of political necessity. That’s generally how politicians do change, if at all. If Mr. Cantor had stood up and declared his fealty to tea-party principles, his critics would have denounced him for ideological rigidity. Mr. Cantor appears to have drawn the right lesson from his party’s defeat in 2012: Self-interest dictates a move to the center. Whether that move is real or apparent at this stage is less important than its direction.

What’s more, to the extent that Mr. Cantor offered some actual ideas to back up his rhetoric, they deserve an assessment on the merits. Some, alas, were ripped out of the old anti-tax GOP playbook — for example, repealing the modest medical device tax that helps finance Obamacare. Others were more promising — federal support for school choice — but also not new.

On one issue, however — reforming Medicare — Mr. Cantor did better. The program’s structure, he noted, is still rooted in the standard Blue Cross and Blue Shield plan of 1965, with an “arbitrary division” between insurance for hospital services and for doctor services. Each side has its own premium, deductible and co-pay rules, which creates expensive complexity, sometimes inadequate protection against catastrophic costs and powerful incentives to seek supplemental “Medigap” insurance. Mr. Cantor suggested unifying the program and revising the cost-sharing rules to create “reasonable and predictable” out-of-pocket expenses.

A 2011 Congressional Budget Office report suggested that such a plan, coupled with limitations on Medigap insurance, could save $93 billion over 10 years. The CBO found that out-of-pocket spending for about half of Medicare beneficiaries would go down or stay the same; the other half would pay more. Obviously, Congress would have to be sure that the extra burden fell mostly on those who could afford to bear it. But it would also have to factor in the substantial benefits of a Medicare that is more transparent, more rational and, above all, more sustainable.

Though Mr. Cantor is not the first authority to embrace such a plan — the National Bipartisan Commission on the Future of Medicare had a version in 1999 — he did give it new prominence. Notable, too, is what Mr. Cantor did not say: He offered no reiteration of “premium support,” the GOP’s erstwhile plan to convert Medicare into a subsidy to buy private insurance. Whatever the merits of that idea, it is, for now, a political nonstarter. If Mr. Cantor is willing to talk seriously about Medicare reforms that might pass in the here and now, President Obama and congressional Democrats should listen.