Sadly for many living in poverty, the chips are stacked against them. From broken homes to hunger, to poor parenting to a plethora of other problems, children from these families suffer lower learning skills, self esteem, and test scores compared to more affluent children among us. The statistics don't lie. But they can be defeated by striving to be, and do, the best for your child when they attend school. Good luck.
I guess it would depend on how long you stay on public assistance. Just a few years shouldn't be an issue. If that's going to be your livelihood you're always going to struggle financially and you won't set a good example for your children.
Public assistance is aiding you and your children at this time. As long as you are a responsible parent and are not abusing "the system" in my opinion, I do not understand why your children would be affected. Everyone goes through hard times, that's life, and it is fortunate programs exist to assist. Best of luck to you and may you get back on your feet soon.
Abs, the biggest way your children will be affected is in school. They used to track children academically, nowadays they track them via the free lunch program and if your child is in it, teachers tend to not expect much from them which sets them up to be low performers