A very good and valid question.
At heart that moral obligation would be to work and contribute, if able to do so. It would also be to raise kids to be capable, responsible adults as well, if one were a single parent with children.
The actual data we have, not anecdotal bull mind you, but actual data, is that the vast majority of welfare recipients don't stay on welfare for long.
The real problem with our social safety net is not that there is too much, but there is too little.
Simply handing someone a check doesn't work well. The heart of welfare reform added work-training, and other sevices, and I am all for that. I think that adding daycare vouchers to that mix would help enormously.
Expensive? Yes. But less expensive than the alternative to letting poor parents flounder, which is that of kids we are then forced to incarcerate at an even greater expense.
Is the current system abused? Yes. Any system will be, public or private. That is simply the cost of doing what is right. A good system will seek some checks and audit systems to minimize that.