Bauler is probably most known for uttering the now infamous line "Chicago ain't ready for reform yet!" (often misquoted without the "yet") after the 1955 election of Chicago Mayor Richard J. Daley.
Bauler was also noted for altercations with Yippie party leader Abbie Hoffman during the tumultuous year of 1968. Hoffman, every bit as an enigmatic figure as Paddy Bauler, had wreaked havoc amongst the Chicago democratic machine politics of Chicago during the 1968 Democratic Party Convention, allegedly threatening to dump LSD into the city water supply, as well as to pull down Hubert Humphrey's pants. Bauler's enthusiastic cry of electoral triumph has come to symbolize Chicago's historic and on going struggles with political corruption. Suffice it to say, recent champions of political rectitude and historic re enactments, such as Milorad R. "Rod" Blagojevich and George Ryan have kept the tradition alive and well.
In case anyone is counting, that makes six governors that have been charged with crimes during or after their terms in offense (oops... I mean office).
Not surprisingly, Bauler was very much entwined in the Chicago political machine throughout his reign as alderman supreme. According to his article "FATHERS, SONS AND UNHOLY GHOSTS", James L. Merriner notes that "Two of his (Bauler's) brothers were aldermen, another brother was a cop, his son was a sanitation superintendent, and anyone else even distantly related seemed to get city jobs somehow."
Ultimately, Bauler's contributions to the political culture were minimal beyond his use of patronage as he pushed for few legislative changes and general disdained reformers, calling one particularly bothersome reformer "so dumb he probably thinks the forest preserve is some kind of jelly" (quote thanks to David K. Fremon's "Chicago Politics, ward by ward" )