He's famous for believing that animals have rights (relax, I'm an animal lover), but he's not convinced that (all) human beings have such rights. If they're more trouble than he determines they should be, they're candidates for termination. (See Singer material on Wikipedia: http://en.wikipedia.org/wiki/Peter_Singer)
Obama's comments on the "democratic decisions" (made by government employees and not including patients, their own doctors, their families, and their priests, rabbis, or ministers!) about when to deny care to terminal patients, truly was chilling. It didn't get a lot of attention from the media. He was saying what many people on the agnostic Left are thinking.
It's not a paradox but rather a contradiction: In order to provide care, excessive in many cases, to all, government must deny it to the some, and the sick elderly are the first ones who will lose.
I'm not under any illusions that end-of-life issues are easy.
Personally, I'm in favor of hospices and DNRs (Do Not Resuscitate forms signed by patients or their next-of-kin), as long as it isn't some bureaucrat signing the DNR. The problem with Obama's "statistical" approach to health care is that it turns out the statistics don't really apply to unique individuals.
As for Prof. Singer, his reasoning about it's being okay to euthanize severely handicapped people is a lot like some of the "moderately evil" Nazis, who looked at handicapped individuals (and other groups) as merely a cost-benefit question. In doing so, they were "enablers" for the "pure evil" Nazis.
Obama-care is going to impose unsustainable costs on the health care system, including payoffs to SEIU members (many of whom are hospital workers) and "cooperative" providers. Also, more and more patients are going to start demanding the Mayo Clinic or Johns Hopkins rather than their local hospital. That will cause costs to skyrocket.
Soon after, the government rationing will begin. The good news will be that we'll all have a "health care" card; the bad news it will be worth less and less.