Alan brought up the critique that conservative-libertarians usually prefer that decision-making be as localized as possible in order to restrain the growth of centralized power. It's a good critique. We remain mindful of it. However, conservatives (and libertarians, I think) are also quite attached to slippery-slope arguments. I'll go out on a limb and try to portray the angle of this one for our readers and writers.
1. America watches Terri Schiavo die over a prolonged period from dehydration/starvation.
2. More attention is paid by everyone to things like living wills and other legal instruments. More commonly, husbands and wives will be explicit with each other about detailed situations.
3. Many will stop and ask, why did Terri have to die of dehydration? Why couldn't she have been well-cared for to the end and finally delivered via an overdose of morphine or some other quick, painless finisher?
4. The euthanasia movement will gain significant momentum.
5. Assisted suicide will either be legalized in a significant portion of the states or the Supreme Court will federalize the issue as they have abortion.
6. America attains the moral status of say, the Netherlands.
Whether this is a pretty picture or not depends on your own moral compass. I'm concerned about where the slope will lead us. I can easily envision euthanasia being actively urged for imperfect infants of all kinds. The Down Syndrome children who aren't already killed in utero via programs to "reduce birth defects" will now be wiped out en masse in their first 10 days of life as parents take the easy way out. We'll start hearing about post-euthanasia parents just like we hear about post-abortive women. Our moral fiber will continue to weaken as we dispose of our challenges instead of growing through them.