Douglas Harper's Etymology Dictionary
type of stereotypical black roles in Hollywood, or in popular culture generally, from stage name (a play on step and fetch it) of popular black vaudeville actor Lincoln Theodore Perry (1902-1985), who first appeared in films under that name in "In Old Kentucky" (1927). Perry said he took the name from a racehorse on which he'd won some money.
Wikipedia
Lincoln Theodore Monroe Andrew Perry (May 30, 1902 – November 19, 1985), better known by the stage name Stepin Fetchit, was an American comedian and film actor, who had his greatest fame throughout the 1930s. In films and on stage, the persona of Stepin Fetchit was billed as "the Laziest Man in the World".
Perry parlayed the Fetchit persona into a successful film career and became a millionaire. He was the first black actor to do so. He was also the first black actor to receive featured screen credit in a film.
Perry's film career slowed after 1939, and after 1953 nearly stopped altogether. Around that time, the actor and the character began to be seen by black Americans and Americans at large as an embarrassing and harmful anachronism, echoing and perpetuating negative stereotypes. In more recent years the Stepin Fetchit character has undergone a re-evaluation by some scholars, who view him as an embodiment of the trickster archetype.
Usage examples of "stepin fetchit".
If he had to shuffle and smile and do his best Stepin Fetchit for the white man, he ought at least to be comfortable.
There were letters to me, comparing me unfavorably to both Richard Speck and the late Stepin Fetchit, but in all honesty it really didn’.
Fagin left, Ying's sweeping slowed till the broom was barely moving, no longer quite touching the floor, a Chinese Stepin Fetchit.
They make him step like Stepin Fetchit and feed him fettuccine with the Cuban kitchen crew.
His voice was abnormally high and silky, but very cultured, sort of as if Stepin Fetchit had gone to Harvard.
Of course, it would be easier if we could get us a hypnoscan and get rid of that Stepin Fetchit accent of yours-it would be real convenient if the two of you were interchangeable-but that's why they made sure you had it.
Danny Dew shouted, grinning, looking a little bit like Stepin Fetchit.
Jackson nodded and smiled and shuffled his feet, putting on a bit of that refined Stepin Fetchit routine which he used to such great effect at the White House.
Might as well segue into one of those grotesque Stepin Fetchit routines from old movies, do a double take and roll his eyes and shag his arms at his sides and howl, Feets don't fail me now.