When did “the American family” rhetoric begin?

[Agonized-Statism]

Actually, more recently than you would think. "Family values" as a political term dates back to its appearance on the Republican platform in 1976, and the nuclear family itself only became the most common form in the US in the 1960s and 1970s before steadily declining. The rhetoric only started up when the ideal of a breadwinning father, homemaking mother, and two or three children was challenged at that time.

This ideal depended on a certain level of industrialization, urbanization, and wages to be practical for the masses despite having existed in some form for centuries going back to Europe, and it was imposed in a big way on Post-World War II US society, when the economic expansion and baby boom created more nuclear families than ever. Socioeconomic power was concentrated in the hands of Greatest Generation war veterans, their wives, and their Baby Boomer children. Corporations and politicians naturally began to craft their messaging for this huge and unprecedentedly prosperous demographic, and that invisibly enforced suburbia left a lasting impression on people who experienced it.