Do you have a citation that the US federal minimium wage ever had the objective that "a single person working full-time will earn enough to support a household of four" because I can't find it in the Wikipedia entry[1] or other top level search results. I also don't see this idea in the 1956 Republican Party platform[2]. At best from reading a few other sources it looks like at its peak in the late 1960s it would have been enough to keep a family of three above the poverty line (though that hardly implies they could afford a mortgage and higher education).

  [1] https://en.wikipedia.org/wiki/Minimum_wage_in_the_United_States
  [2] https://www.presidency.ucsb.edu/documents/republican-party-platform-1956