I am not sure the poor get as much free stuff as you think they do, and you have to be really poor to get any free stuff, as far as I know. There are plenty of people who do not qualify for any assistance, or for very limited assistance (like maybe CHIP for the kids), and who have trouble paying for childcare.
Other than that, I agree with you that many people are being seriously squeezed and that many women who choose to SAH do so because it simply would not pay for them to work and shell out for DC or because the DC they can afford is sub-standard.