What program decreased in popularity as the public began to believe that it was encouraging out-of-wedlock births?

I believe the answer is: Aid to Families with Dependent Children

Aid to Families with Dependent Children is a government program that created to aid the children from a family that has very little to no income.
Since the majority recepients of this aid is most likely teenage single mothers, many people see this as the act that encourage out of wedlock births.

The  ancient egyptians  who  built the pyramids  may have been  able  to move massive stone blocks across the desert by wetting the sand in front of a contraption  built  to pull the heavy objects