One of the main rationales behind welfare reform was the view that teenage single moms are irresponsible. Since their predicament is in large part the result of their own high-risk behavior, they're less deserving of help than, say, the congenitally blind.
This rationale seems right to me. It is irresponsible to have a child who you aren't able to financially support, and irresponsible people are less deserving of help.
Now consider: One of the main stumbling blocks to Social Security reform is the view that left to their own devices, many people will fail to save for their own retirement, and "we as a society" can't allow them to live in poverty. Objectively speaking, however, there is a strong case that people who fail to save for their own retirement are much more irresponsible than teenage single moms.
How so? You can become a teenage single mom just by yielding to impulse once. And once you have a child, it takes two decades of hard work to make up for your youthful indiscretion. I won't say "It could happen to anyone," but there are a lot of responsible adults out there who are lucky that their risky teen-age behavior didn't happen to mess up their lives.
In contrast, no one fails to save for his retirement because of a few minutes of teen-age passion. To fail to save for your retirement, you need to make the wrong decision week after week, year after year. If you're too immature to save for your retirement in your twenties, you have a second chance in your thirties, a third chance in your forties, and so on. In short, to fail to save for your retirement, you have to be consistently irresponsible for decades.
The upshot is that the moral objection to Social Security reform is greatly overstated. Elderly people who fail to save for their retirement are at least as much to blame for their plight as teenage single moms. My Non-Bleeding-Heart Libertarian view is that both groups should have to rely on family and private charity. But if that's too harsh for you, there's still every reason to make old-age payments as stingy, means-tested, and stigmatized as welfare payments. Indeed, since failing to save for forty years is a lot more irresponsible than failing to use birth control a few times when you were sixteen, there's every reason to make old-age payments more stingy, means-tested, and stigmatized than welfare payments.