I took that quote directly from your post.
I said "Welfare and food stamps help the poor but they also doom them to stasis."
I addressed this, and I asked for a source because I am interested.
The research I have seen, for some of which I provided links, refutes the idea that people are generally stuck at the bottom if they accept welfare.
For example, assistance that is contingent on being employed or looking for work is especially effective at increasing the work and earnings of female-headed families (the most over-represented group among working poor), and boosting the school achievement and college attendance rates of their children.
I submit that anyone who's been "doomed to stasis" by accepting help was never likely to do any better, and probably much worse, without that help.
I did say that the minimum wage doesn't help the poor. It helps people who already have jobs by establishing a price floor on wages. But your truly poor don't have jobs and so can't benefit from the price floor. For those unemployed individuals looking for work, the minimum wage drives the unskilled labor out of most of the job market unless they possess skills worth the minimum wage.
Who are the truly poor who don't have jobs? As I said, 90%+ of people on welfare are either working, elderly, or disabled.
As for the individuals who are of the working poor, the minimum wage doesn't help them either. It doesn't position them to do anything but subsistence living. The people who benefit most from a minimum wage are people with skills who can expect higher wages because the minimum wage is what you pay the unskilled so the skilled can demand more.
Once again, this doesn't appear to be supported by facts. Even the cbo report mentions an increased mw to $10.10 would result in 16.1M people receiving higher wages, 1M people being lifted out of poverty, and 500K possible job losses which would be offset partially by increased demand and people dropping their second jobs. Sounds helpful to me.
I don't know what you mean by "positioning them for subsistence living". First and foremost, people need to be able to make a living.
I try to keep in mind that, even if mom is a low wage earner for the rest of her life, her kids getting an education and doing better because they are well fed, happy, healthy, and have a mom that can spend time at home, the result is a positive roi.