Not that this is the end all be all, but even Hayek argued that a country as rich as ours can afford to have welfare programs to support the poor. But he also made the argument they shouldn't have all the choices someone not supported by welfare should, i.e. no doritos and mountain dew on the food stamps, probably no cancer treatment, etc.
I personally have no problems with welfare programs, other than the government treating them like handouts to corporations, i.e. no negotiations on prescription drug costs. I'd rather see see these programs ran on the state level to avoid putting money in the federal government's hand, and also to allow for competition between states to make these programs more efficient. I'm not advocating for guaranteed paychecks like Stein is and I disagree with minimum wage laws and other central economic planning, but providing people who couldn't afford otherwise food and reasonably limited healthcare is something I support. Even if it is their own mistakes/choices that led them to the situation they are in. I just don't see much difference between providing welfare and providing the protections like police, judges, and the laws that protect our liberties.
I don't think most people have a problem with a safety net. I prefer a very small safety net where the government is only involved when the free market can't handle the problem. The problem most people here have with safety nets, is right now there is a safety net for every damn thing. Its so severe, people just prefer the safety net than taking their chances with the free market. Now that is a problem. Government safety nets should not be providing more benefits than the free market.