Most of the women surveyed also said they agreed with the statement that the family cap encouraged people to take responsibility for their actions.
Thus the family cap will not significantly reduce illegitimate children or welfare costs.
Specifically, family caps were found to increase the poverty rate of children by 13.1%.
That group sued last week, saying the family cap punished children because of their parents' decision to reproduce.
Before the family cap, welfare recipients received approximately $64 a month more for each additional child.
The family cap applies regardless of the number of children.
But opponents argued that the family cap punished children for the mistakes of their parents.
The provision is widely but unofficially known as a family cap.
But states could override this "family cap" with a vote by their state legislatures.
Some families qualify for a complete subsidy, others pay $25 a child a year, with a family cap of $100.