My problem with it, having been a recipient when I was a kid, is that it's pretty well all or nothing. If both of your parents are rendered unemployed like mine were back in the 80s when my dad was laid off and my mom went into a deep depression, welfare does its job fairly well. However, there's a little bit of a sliding scale but then it just kind of goes away, as it did when my dad got a job as a maintenance man at the apartment complex we lived at at the time. There's not a lot of positive incentive for people to take that first step towards getting back on their feet.
There is, on the other hand, a great deal of negative incentive. Much of the lingering conservative outcry over welfare was drummed out by the Republican Congress and Bill Clinton in the 90s. It now has a time limit and recipients are expected to retrain themselves for new jobs while they're on the government dole. It's really not all that easy to leech off the system anymore, even if you have a lot of kids; there just aren't all that many "welfare queens" out there anymore.
The real issue with Medicare, let's face it, is that it provides a level of service to old people that everyone should be getting. However, if we try to expand it, those old assholes turn right around and scream "SOCIALIZED MEDICINE" at the top of their lungs until we half-ass our way into a Republican-sponsored system that the Republicans suddenly don't like anymore due to some sort of reverse Your Brother's Toy situation.