there's a big difference between a welfare state and full out socialism; the difference is largely about power... Socialisim is about giving the workers control over the means of production. The welfare state is merely about seeing to it that people don't starve.
We're rich enough, in America, at least, that with tax increases, we could provide the minimum for everyone, and pay for it out of the sorts of taxes we pay now (only, of couse, somewhat more)
There was a lot of effort in that direction here and in the UK in the '70s; there was a lot of criticism that the public housing, for instance, wasn't very nice, but what really ended it was the rise of the political movement that backed Thatcher (in the UK) and Reagan (in the US)