The working poor are poor due to unemployment or low-wage jobs. Try making ends meet with subsistence level pay and no benefits. One major medical bill and you're on the way to homelessness.
The solution isn't providing mandatory minimum wage jobs with no benefits — basically a safety net with very large holes.
The working poor are "dependent" to the extent that they depend on employers who make hundreds of times what the average worker takes home.
Ideally, a solution would involve fair-wage jobs, i.e., ones that provided enough income to pay for a modest home and feed and clothe one's family.
If a corporation cannot or will not pay a fair wage, an earned income tax credit (a negative income tax) would take effect to supplement the low salary. That would result in a living wage for the worker.
In addition, single-payer universal health care is something that should be a offered by any civilized society.
The United States is not a nation of dependence so much as it is a nation of the very wealthy and the rest of us.