At one time, many polls asked people for their occupations, which were then coded into groups. For example, Gallup used to classify people as farmers; business, executives; clerical; sales workers; skilled workers; unskilled workers, operatives; service workers; farm laborers; laborers, except farm and mine; and professional. They stopped around 1970. Since then, most surveys have asked about education and income, but not about occupation, so the "working class" is defined as people with low education or income. Thomas Edsall refers to a new survey by the Public Religion Research Institute that takes a different approach: it includes a question on how people are paid and defines the working class as people who are paid by the hour or the job and do not have a college degree.
How much does it matter how you define the working class? A 2006 survey from the Pew Research Center makes it possible to compare. It didn't ask people for their exact occupation, but asked them to pick from ten groups: professional; manager; business owner (two or more employees); clerical worker; sales worker; sales representative; service worker; skilled trade; semi-skilled; and laborer. It also asked people how they were paid and the usual questions on education and income. Unfortunately, the survey had few questions on politics, but it did ask about party preference. I restricted the analysis to whites and looked at party preference among the "working class." Of all whites, 39% said they were Democrats, and 45% said that they were Republicans, which can be summarized as -6 (39-45). The party preference of "working class whites," using several definitions:
No college degree -6
Income under $50,000 +6
not salaried 0
not salaried & no degree +3
manual or lower non-manual job 0
Defined by education, the mix of Democrats and Republicans in the working class was no different than the middle class. Defined by income, the Democrats had a lead in the working class (44%-39%) but were well behind in the middle class (39%-51%). With the other definitions, the Democrats do better in the working class, although the gap is smaller than when defined by income.
There's some overlap between the different "working classes," but it's far from perfect. For example, about 40% of people in "white-collar" occupations (which I defined as professionals, managers, business owners, and sales representatives) lacked a college degree and about 20% of people in "working-class" occupations had one.
No matter which definition you use, the Democrats do at least as well among "working-class whites" as among middle-class whites. Of course, you might argue that none of the differences are as big as they would be if working-class whites (or maybe middle-class whites) were following their class interests. But on a basic level, the Democrats don't have a particular weakness among working class whites.