Ability to pay with proof the person is trying to get a job, should be considered. Whether or not the man was actually the biological father should also be considered. And if the man takes custody the woman should be equally liable for child support.
In cases where there is no other parent who has money to help raise the child the government should pitch in and pay the child support. Children shouldn't get special privileges just because they happen to have an absent parent that can afford to pay child support.
In cases of ordering payment of back child support where the child is now an adult all the money should go to the now-adult child, not either of the now-adult child's parents.