We could have dealt with this years ago, even back when Clinton took credit for "reforming" welfare. It's simple. Just put a two-child limit on benefits, effective some day about 10 months from now. Get pregnant tomorrow? No bennies for that baby, sorry.
If you're already getting benefits for six or 10 kids, well, we taxpayers may be stuck with their care and feeding, but there's no reason not to turn off the tap before potential mothers create another mouth to feed.