The problem is that a lot of welfare programs are means tested. So if your income goes up by a dollar, each of your 4 welfare benefits might be reduced by $0.30. So it sticks people in these plateaus where there is a substantial required jump in income needed to actually increase disposable cash.
I worked for a short time at a gas station, while having unemployment. The job paid minimum wage, and had no benefits or perks.
The first thing: when reporting wages, you had to report the untaxed amount to unemployment, even though I never saw that. I only received 87% of what I was paid.
Second: I now have wonderful costs, like driving to work, wear and tear, and other costs associated to working. This lowers my effective 87% even lower.
Third, I was on foodstamps. The moment I touched a job, which reduced my benefit by amount before taxes, I also had deducted from my foodstamp balance. I'm now down, by 2:1.
So, I did what many do in my situation: dump the job and go to school. I have less of a problem with myself with taking public assistance if I better myself.
The even bigger problem is parents. As long as you have no job, you don't need any help taking care of your kids. As soon as you have a job you find that a huge chunk of your income goes towards taking care of your kids.
Its worse than that. If you go over a certain threshold you might no longer qualify for certain types of assistance that are worth a lot more than that threshold, healthcare especially.