Strictly speaking, Republicans aren't trying to push old people off a cliff. They're trying to persuade them to wheel themselves.
Weirdly, the argument being made by some is that the Paul Ryan plan not eliminating Medicare. It's merely putting tax money into the hands of seniors so they can choose their own plan. If this sounds familiar it's because it's the part of "Obamacare" that they insist is SOCIALISM!!!!111!!! Seniors would then, because the money is capped in a way that it isn't now, would be forced to shop around and therefore, market prices would drive down the price of medical care.
Much in the same way that Medical Prices are low now because people can shop around. Oh, they aren't low? Well, they would be. And seniors would have the upper hand in the deal because if they can't get a deal they like, they can just walk away from the negotiation.
(descending slide whistle; CRASH)
Well, I hope the Republicans keep pushing the plan right up to the edge of the next presidential election.