This, exactly. If we want to discourage people from having children that we'll all have to support, do it via encouragement, support, reward. Require work from welfare recipients, and make that work pay slightly better than welfare. Provide easily accessible free birth control, reproductive counseling, child care so that people on welfare have an easier time training for or looking for work. Make payments lower for successive children. Generally work to make it so there is less financial incentive to have additional children and more financial incentive (and fewer impediments) to be a responsible, productive individual. There is no amount of potential saving that would justify forced sterilization, even temporarily.