The most commonly cited unintended consequence of such policies is, ironically enough, continuing poverty. Conservatives argue that such programs actually encourage people to remain poor. They argue that these programs make it easier for people to allow the programs to support them than it is for them to go out and get jobs. This leads to a "culture of poverty" in which people do not learn the skills and attitudes needed to get them out of poverty.
A second unintended consequence might be the increase of the overall size of the "welfare state" in the US. When people see the poor getting what they call "handouts" they want the government to help them as well. This leads to a situation like we have now in which various levels of society all want government to help them even as they want to pay lower taxes. Thus, anti-poverty programs create a greater level of demand for government programs to help all levels of society. That, of course, leads to a ballooning in the size of the government.