What does "weed out" mean exactly. Would you provide these people with the minimum needed to live or would you stop all benefits entirely. I have no problem with reducing them to the basics but do not see it as a simple "to pay or not to pay" problem. I would be looking for initiatives to address the underlying problems and I'd also be looking to raise minimum wages so the difference between welfare and wage does make it woth while.
But - as I understand it the problem in America today is not there are lots of jobs but the lazy buggers won't take them. The problem is there are not enough jobs because the greedy bankers screwed up the economy. I would not even bother trying to address the problem of the dont-wanna-job when there are millions of do-wanna-jobs out there and not enough jobs for them.