I haven't seen Lebowski, but the statement above is quite inaccurate with respect to the other movies. (Blood Simple, Raising Arizona, Fargo, & Barton Fink).
The Coens use working-class characters to tell their stories, which are about the world, not the w.c.
In Blood Simple, the most sympathetic and successful character is the plucky, working-class woman (McDormand), in contrast to the slimy bar owner and private dick. The dominant mechanism in the move, however, is that nobody quite understands what's going on at any particular moment, notwithstanding the riskiness of the situations they get into.
In Raising Arizona, the characters come from three classes, so to speak--the rich, the w.c., and the lumpen (the motorcycle dude). All three are partially endearing, thanks to their assorted types of loopiness, but the dominant theme is the parody of family values pursued by the w.c. 'heroes.'
Fargo, like Blood Simple, represents the triumph of the everyday, non-flashy person (McDormand again). The criminals are dangerous but pitiously stupid, venal, and unlucky.
Barton Fink has one of the darkest visions of the movie business you could find anywhere.
I'm eagerly awaiting the arrival of The Big Lebowski to my cable station. Mr Cranky needs to find another profession.
MBS