This has 2 issues about it: Children of poor families, and drawing a line somewhere for those being assisted by gov't.
I agree about people who can't support them shouldn't be having kids. I agree with the underlying concept of curtailing unreasonably stupid people from diluting the gene pool. Obviously if it's a gross state of what Evil Q said, something ought ot be done to discourage it. Something ought to be done to discourage future occurrences.
Having said that: before cutting funds, maybe a look into why a family is poor, first? Couldn't hurt. Begin the transition NOW. As to those already existing on gov't. aide, assist those for the time being at least.