Palin and her supporter argue that if health care must be rationed, then some people will be left to die because they are not productive. However, if health care was universal and must be rationed, doctors are not necessarily going to deny care to the elderly or disabled. Even in our current system, those of us that are healthier are put at the top of transplants lists and such, but this does not mean we deny opportunity to those without strong bodies.
They are an example of a 'slippery slope' fallacy - they believe if A happens (health care is universalized) then eventually Z will happen (people will be left to die because they are not 'contributing'). However, this is not absolutely true.