The complaint by South Carolina's less than gentlemanlike lieutenant governor that giveaways to poor people encourage them to breed like "stray animals" leads me to consider what one might do to lower the fertility of poor women if that were one's goal.
Poor women in the US appear to have a higher fertility rate than not so poor women, although this may be skewed by the fact that having children sometimes makes one poor at the same income level that would not qualify as poor for a childfree household. In fact, fertility decreases with affluence with total fertility at just below the replacement rate of 2.1 children per woman. Assuming that the policy goal is to reduce the fertility of the poor, leaving for the later the implications of negative population growth, how might the State of South Carolina go about this?
This could be accomplished by (a) reducing the value of children, and/or (b) increasing the cost of children. Child labor restrictions and other policies render the economic value of children negligible, and it is difficult to imagine how the State of South Carolina could make having children less entertaining and satisfying. Perhaps if the children of the poor were required to attend boarding school away from their parents they would be less fun to have, but the cost of such a solution and its questionable constitutionality argue against it. Accordingly, the State of South Carolina is left with the cost side of the ledger.
Pronatal subsidies such as free public schooling, tax credits and exemptions, AFDC, WIC, and the like reduce the cost of childrearing, albeit at levels that are unlikely to have a significant impact on fertility except at the margins. Poor people reproduced at even higher rates before these programs were in place and continue to do so in countries without such subsidies. It is probably not possible to limit free public schooling to persons of means, but it may be possible to have the same impact by charging school fees while keeping attendance mandatory. Enforcement of such a measure, eg by incarcerating recalcitrant parents, would be costly and interfere with other state goals.
The best way to increase the costs of childrearing would be to increase opportunity costs significantly by ensuring that women actually have meaningful opportunities to forego. Then again, this may well entail wholesale changes to the systems in place in South Carolina that lead to the existing poverty rate and permit the advancement of politicians of the sort who reckon that the reduction of the fertility of the poor is a legitimate goal.