I have a feeling this discussion is going to quickly devolve into libertarian "non-aggression principle," fairy tale land discussion of "natural rights," so let's just deal with that right away. We create rights and we take rights away. Many used to believe there was a "natural right" to own other human beings. Did you know that no holy book with which I'm familiar, including the Bible, mentions the word "rights" at any point? Did you know that the Constitution makes clear in its 9th Amendment that the people may declare new rights and protect those rights in the future?
If you believe we should be protecting human life, it entails more than having a police force and an army and anti-abortion laws. Clearly, life is also protected by the treatment of sickness and disease. The position of a minority is, "Tough luck. You should've thought of that before you were born to derelict parents and with below-average intelligence." Or, "You should've thought of that before you made those poor choices. You deserve to die, short of private charity helping you out." I would submit that a culture cloaked in Judeo-Christian values isn't likely to go down the social Darwinist, John Galt-Mad Max World, everyone-for-themselves route anytime soon.
If you believe private charities and churches adequately provided for the needs of the underclass prior to welfare programs, you're historically-misinformed. It was especially harsh on children (and the aged). Those institutions would be even less-equipped today to take on such a gargantuan task. We have a growing underclass where more-and-more of them have no place in our economy. Many are just above being mildly retarded in an economy where an increasing number of low-paying jobs require more and more reasoning ability. Add to that an immigration system that lets in millions of similarly low-skilled workers and you have a recipe for disaster. So what are you going to do for them? They're on their own? How about their kids? Are they on their own, too? Private charities and churches cannot provide healthcare to all/most of them. They should've thought of that before they ended up in this situation? They'll continue to end up at ERs. Then we all pay for it by delivering their healthcare to them in the most inefficient way possible. We end up paying their healthcare bills one way or the other. Which way would you prefer?