We don't know if they can't get jobs, all we can do is speculate about what might happen if they looked. Health care is also available, it's called medicaid.
So basically, your only correct complaint is that our educational system is broken.
You seem to suspect that poor people are lazy to the point of being irrational. I disagree. If there were sufficient rewards for them to work-- a way out of poverty would be a huge reward-- then they would. However, there is no such work available to them. Otherwise, they'd be likely to take it.
http://www.bls.gov/cps/cpswp2007.pdf
We don't know if they can't get jobs, all we can do is speculate about what might happen if they looked. Health care is also available, it's called medicaid.
So basically, your only correct complaint is that our educational system is broken.