Paul Krugman wades into the debate over whether Republicans did indeed vote to end Medicare:
I’ll just quote the blogger Duncan Black, who summarizes this as saying that “when we replace the Marines with a pizza, we’ll call the pizza the Marines.” The point is that you can name the new program Medicare, but it’s an entirely different program — call it Vouchercare — that would offer nothing like the coverage that the elderly now receive. (Republicans get huffy when you call their plan a voucher scheme, but that’s exactly what it is.)
Medicare is a government-run insurance system that directly pays health-care providers. Vouchercare would cut checks to insurance companies instead. Specifically, the program would pay a fixed amount toward private health insurance — higher for the poor, lower for the rich, but not varying at all with the actual level of premiums. If you couldn’t afford a policy adequate for your needs, even with the voucher, that would be your problem.
I mostly, but not entirely, agree. There's a continuum here among potential changes to the program. At one end, you could argue that even small reforms constitute "ending Medicare." The Affordable Care Act tries to rationalize the incentives and payment structure of the system. I wouldn't call that "ending Medicare," but it certainly changes the program from one thing into something different. A more powerful version of the ACA reforms could more properly be called "ending Medicare" -- or, at least, bring us closer to the point where that label would be fair.
At the other end of the continuum, if you replaced Medicare with a program to give every retiree a bottle of aspirin and $10 off their next doctors' visit, that would be "ending Medicare," even if some right-wing think-tank shoved out a paper claiming that this would somehow lead to old people leading healthier lives.
In between, you have a gray area where you can legitimately debate whether a change constitutes ending Medicare. Now, I think the charge as applied to the GOP budget happens to be fair. But it's a matter of interpretation, not fact. Republicans have tried to get the news media to treat this claim as a falsehood, like death panels. It clearly is not that. But the Republican defense is also not a total absurdity along the lines of calling a pizza "the Marines." The Republicans have a plausible argument that their proposal does not mean ending Medicare. I don't buy the argument, but this is a proper matter of dispute, not a question where fact-checkers can provide us with a clear-cut answer.