Cheryl,
I read your question several hours ago, and I've been thinking about it all day. I had to respond.
I read your SWH and I have to say, I drew some of the same political conclusions as some other posters. I suspect that is because I have read at least one (though I think I remember more) posting/question from you about how you are working toward reforming the welfare system in your state. I think I recall you mentioning that your plan for reform included a provision for benefits stopping if a W. becomes pregnant while on welfare. I think that was in the back of my mind while I read this question, and that it factored into my answer. Since, however that is apparently not what you intended with your question, I will try to answer it as you wrote it.
Yes, ideally financial stability should factor into a decision to have children. You should be able to feed, clothe and house your offspring on your dime. The rest is less black and white. I have no problem with my tax dollars supporting the medical care of low-income children, or with the government (again, with our taxes) subsidizing college.
For me, it was the other questions you raised in your post, about paternal responsibility that bothered me. The idea that a man should be off the hook financially because he stated a that he didn't want kids is crazy to me. Why should the child suffer because his father isn't interested in paying child support? I might say that I don't want to get into a car accident, and I may tell everyone in my path my preference, but the moment I get in that car and start driving around, I have assumed the risk that an accident may result. Sex is no different. If he truly doesn't want kids, he shouldn't engage in the behavior that produces them. If he chooses to have sex anyway, he needs to take precautions to prevent pregnancy, which means he gets a vasectomy, or wears a condom, every time, and that he accepts that even with these precautions, there is some risk of pregnancy.
I don't think that expecting men to be financially responsible for the children they produce is "trapping" them in any way. The way babies are made is not some female-held secret that we don't let the boys in on until after they have knocked us up. That would be a trap. This is simply a part of life, we make choices and we are responsible for the consequences of our choices.