I'm asking you, is this really such a big problem that it requires getting rid of welfare? Is the US financially in trouble because it pays out welfare to undeserving layabouts? I seriously doubt it.
There is a somewhat intermediate of this, proposed by Milton Friedman, called the negative income tax. I can't say I'm sold on the idea but it does solve some of the problems of the local maximums encountered that keep people trapped in the welfare system and from trying to get more lucrative income.