Can you have a middle class without middle-class jobs?

From David Autor's paper, "The Polarization of Job Opportunities in the U.S. Labor Market" (pdf):

The structure of job opportunities in the United States has sharply polarized over the past two decades, with expanding job opportunities in both high-skill, high-wage occupations and low-skill, low wage occupations, coupled with contracting opportunities in middle-wage, middle-skill white-collar and blue-collar jobs. Concretely, employment and earnings are rising in both high education professional, technical, and managerial occupations and, since the late 1980s, in low-education food service, personal care, and protective service occupations. Conversely, job opportunities are declining in both middle skill, white collar clerical, administrative, and sales occupations and in middle-skill, blue-collar production, craft, and operative occupations.

Take a look (click for a larger version):