That's a real mystery. Illinois had been a solidly Republican state before that 1932-1948 stretch and its flip could be looked at as a return to form, but that doesn't explain the margins. Stevenson did terribly for a relatively popular incumbent governor, and a member of a distinguished Illinois political family no less. Nor did Eisenhower have some special appeal there- it was a Taft state in the Republican primaries. The statewide races were uneventful too, so no answers there.
My guess is McCarthyism-influenced backlash against the Chicago political machine. Theirs was the last big city machine left after James Farley nationalized the patronage system and immigrants rapidly became assimilated, prosperous, and no longer in need of extralegal aid in the 1940s, so it would have been a localized event. Cook County particularly was suburbanizing rapidly during that time with the availability of FHA and VA insured loans, the construction of thousands of single-family houses in Skokie and Oak Lawn, new expressways, and the move of many businesses to suburban locations. Also worth noting toward this theory is that Kefauver won the nearby Minnesota primary in 1956 by portraying Stevenson as a captive of corrupt Chicago political bosses.
I also think that Eisenhower probably did respectively even among nominally working class
Democrats in Chicago who would have voted D down ballot because while they may have liked Stevenson at the gubernatorial level wanted change after twenty years of Democratic rule in the White House. Stevenson also underperformed among black voters nationally because his runningmate was a known segregationist and I imagine this had a particular impact in Chicago.
