Most well known stereotype exhibiting a Grabowski is the Saturday Night Live skit, "Da Superfans," which makes fun of the Chicago accent, love of "Da Bears," "Da Coach," "Ditka" and love of Maxwell Street Polish Sausage, all of which a proper Grabowski is known to love.
Possible etymology might reference Jim Grabowski, the star running back who played at Taft High school on the Northwest side of Chicago, then starred as running back at the University of Illinois Urbana-Champaign. He played professionally for the Green Bay Packers and the Chicago Bears in his final season, from 1966-1971. He then went on as a radio color analyst for the Illini, until the 2007 season. It is unlikely he had the accent on radio.