Murray's key point is that the cultures of our upper middle and lower classes have diverged substantially in the last 50 years, since 1960. He particularly looks at the issues of marriage, single parenthood, industriousness, crime, and religiosity.
On all of these dimensions the two groups have diverged in the last half century. The upper middle class still exhibits what we think of as the American culture, the lower class no longer does.
As a libertarian Murray eschews governmental solutions. Instead he advocates the upper classes "reinforcing" American cultural values in the lower classes:
The best thing that the new upper class can do to provide that reinforcement is to drop its condescending "nonjudgmentalism." Married, educated people who work hard and conscientiously raise their kids shouldn't hesitate to voice their disapproval of those who defy these norms. When it comes to marriage and the work ethic, the new upper class must start preaching what it practices.
It once worked, I wonder if that would work today?