Just want to add that, at least in America, any eugenics program would probably be applied disproportionately to minorities just like poll taxes, drug enforcement, voting laws, etc. due to the deep seated racism the country still has problems with.
Also, all this has all been done before... Birth control has already been offered and coerced on poor women in America by government programs... the intro to this book is a good read:
https://books.google.com/books?id=mBnvelNSpY0C&lpg=PP1&pg=PA3#v=onepage&q&f=false
" ...officials across the country began in the 1920s and 1930s to offer access to reproductive technologies through public health and welfare programs. ... Women gained reproductive control, for example, when state officials began to offer birth control through North Carolina's public health clinics and when, several decades later, state legislators enacted a voluntary sterilization law and liberalized North Carolina's abortion law. ... Women lost reproductive autonomy when social workers threatened pregnant women on welfare with sterilization and attempted to tie offers of financial help to the use of contraceptives."
A quote that really hits a big tension point:
"While all four groups shared the goals of improving infant and maternal health and reducing poverty, they disagreed about women's ability to control their reproduction and the desirability of giving reproductive control to women."
Anyway, if you're interested in this i'd give the free book preview a read.