"But hey, if we toss out Mrs. Jones, think about how much money we'll be saving people whose only interest in Mrs. Jones is preserving the right to call on tax money to save their own beloved elderly, right?"
Puts a whole new spin on it, doesn't it?
I know that I'm going to be labeled a hypocrite for this, but tax money should be spent from more of an investment position, than a consumptive one. Helping my grandmother, for instance make it from 100 to 101 might make me feel really good that I didn't have to cough up the cash myself, but it's not going to put anything back into the society in and of itself. If it's important to me that she live a year longer, then I should be ready to pay the costs it entails.
Life extention for the very elderly might be a laudable idea, but it can also be a form of conspicuous consumption - "Look how much money we can spend on keeping the nonproductive alive!" (And yes, that goes for your terminal cancer patients, as well.)
Someone else refusing to foot that bill is no more euthanasia than not having a world-class trauma center in the middle of a sparsely populated area - will people die because they were too far away from life-saving treatment? Yes. If that's euthanasia, then not having a fully-stocked hospital in every single township in the nation constitutes mass murder on an epic scale.
Anyone being asked to foot the bill SHOULD be allowed to perform a cost-benefit analysis for the funds they are beign asked to spend, if for no other reason than funds are limited. We could easily spend every dime of public money in the country funding medical treatment that would bring slight improvements to people's lives - they fact that we don't means that we're already making decisions about where money is going to go, and where it isn't.