There are a number of ways to respond and think about that question, but a simple way to start is to ask what are your underlying assumptions?  It appears that you are assuming that providing a legal right to die to some people has zero impact on others who would prefer to live under the same, hopeless circumstances. That is, a right to die is independent of a right to live, even if both rights can be traced somehow to the flowery language of the US Declaration of Independence. I question that assumption because it appears to directly contradict everything else we (meaning most people who visit this site regularly) have already implicitly or explicitly professed to believe about how the world works. Namely, we progressives reject the neoclassical assumption of individual omnipotence and omniscience when making choices and acting on them, which underlie all arguments for greater privatization and a very minor role for the state in capitalist society.  

Instead we accept the institutional critique which underlies most "progressive" intellectual endeavors, such as feminism, critical theory, and most "pro-state" ways of approaching economics and other social sciences. In our framework for thinking, individuals have very limited power and knowledge about the world, so their choices are inherently biased by the language and institutional contexts in which they find themselves. "Bounded rationality" is the technical term for how progressive thinkers believe the world works.

So, if you don't believe that free-market economics is the default solution to a social problems such as inequitable distribution of medical care, then you are implicitly rejecting the idea that a truly individual choice to die is even possible.  An individual's options are necessarily bounded by the possibilities presented to that individual by language, values, and other social structures. (That's the essence of the progressive argument against Laissez-faire capitalism.) And if that is the case, then just changing a law to make death a socially acceptable option for hopelessly ill people must also affect, most likely negatively, the ability of similarly hopeless people to choose the socially more inconvenient path of living longer while burdening the community.

Put more simply, I don't believe that the myth of individualism is true. Individual welfare, everywhere and anywhere, is mostly dependent upon relationships with the larger community in which one finds oneself, and inalienable rights are one form of such a relationship in our current, rights-based political institutions.  Therefore, it's not possible to assume that a right to die is independent of a right to live. Rather a right to die necessarily diminishes a right to live, and vice versa.  

And this means, as I said elsewhere in this thread, that legal suicide is simply incompatible with social medicine. It might be compatible with a completely private system of medical care, the Laissez-faire utopia, but I don't believe such a utopia is possible, and you probably don't either.