Remember that the ultimate goal of these programs was not merely to relieve the pain of poverty, but to attack its root causes. The main problems were:
1. That goal eroded almost before it began. The poor don't vote and there are always plausible cover stories to deny them systemic reforms, so they are the first group that gets screwed in every negotiation.
2. Many Americans refused to admit we have a class structure, so social programs get repackaged as entitlements rather than charity. Entitlements balloon in cost and are vulnerable to the demographic trends you cite.
3. It's very easy to pander to racist narratives when poverty correlates with race. Hence the meme of the Chicago welfare queen (who never existed) and the general insistence by white people that they shouldn't have to "subsidize" the "black culture of violence." The irony is the typical recipient of food stamps is the white child of the fundies who vote to "screw those urban animals." The ideologues who oppose social spending stoke this fear to destroy the whole system.
I think people are finally starting to figure out 2. One thing the Great Recession showed us was just how little regard the 1% has for the 99%. The GOP can keep running deceptions like calling this "envy," but that act, long shopworn among the more educated, is even starting to grow old among the (increasingly, unable to find work) working class.
1. is a long term issue that I suspect is tied closely to 3.
3. is a huge. We really need the Martians to attack or something so that people will just cut the crap on race. My hope is miscegenation ultimately makes it completely moot (and gives us a population of
multiracial super models).