Ugh! Why not just fund birth control prescriptions instead of permanent sterilization? That's really all that's needed for those who don't want children, can't afford children, and can't afford birth control. Permanent sterilization DOES smack of eugenics, and also sends the message that nobody expects these people to ever get their lives together and get off welfare...at which time they might be able to afford kids and want them, but then are sterile.
Or, here's another crazy idea...a social support network for the kids to get them into school and to stay in school so they graduate and can get at least a halfway decent job and break the welfare cycle.