But the other side is that they money they are asking for has to be taken from people who were responsible and can afford their families. Shouldn't we at a minimum require that if you seek help for family members you can't afford, that you take the same steps others take to not get any more kids you can't afford?
Because unless you have a good counter argument to that, you won't get anywhere politically.
But ultimately my counterargument would be that we should focus on helping people who need it, rather than on not helping people who we think don't deserve it. This country has a puritanical mindset about public help, where we're outraged at any person who receives it who we see as being in any way unworthy. For a pervasive recent example, look at drug testing for welfare recipients. It's more expensive than not doing it, but people love it because we see drug addicts as being evil and therefore unworthy of help.
We need to teach compassion, or at the very least rationality, rather than a punishment mentality.
We also murder people who have expired tags, as long as they don't pay the fine, don't show up in court, resist the police officers enough to get them to shoot them.
In reality essentially everybody stops before it gets to that point, and in your example the women buys (or ideally gets) a bunch of condoms, use them and no more children nobody can afford is brought into the world, and maybe she also avoids some STDs.
Look I don't want to compel her to do it, but at the very least make sure that she understands that the people who pay for her children have certain justifiable expectations.
>people love it because we see drug addicts as being evil and therefore unworthy of help.
If you work hard at a crap job that pays say 22 usd/hr, you don't want to pay for somebodies meth bill.
If you want a system that can help people then you need it so that it is politically palatable enough -- or you won't be able to focus on it at all.