The prediction was based on the computer revolution being wildly successful. They thought that the labor productivity would increase by automation and cybernation. They also predicted that Americans would be taking 7 or more weeks of vacation each year.
Now that both parents tend to work, there has actually been an increase in working hours per family from 500 to 700 hours more than in the 1970s. Workers are also pushed to get more done in a quicker amount of time. The fact that this prediction didn't come true just shows that our robot overlord are not as good as we thought they were going to be.