When rehearsals started for the original Broadway production of My Fair Lady, Julie Andrews was awful, at least in the portions where Liza was the unscrubbed flower girl. She was reportedly able to play the later scenes where Ms. Doolittle has become a refined lady of apparent breeding but she just couldn't master the character in the early scenes. It was so bad that her co-star, Rex Harrison, threatened to stop coming to rehearsal. He didn't see why he should waste his time rehearsing with an actress who obviously had to be fired and replaced.
In a "last chance" desperation move, director Moss Hart gave everyone but Julie a few days off from rehearsal and went into an intense, one-on-one tutoring session with her. It was brutal, it was exhausting…but it worked. Hart pasted the role on her, doing the opposite of what Henry Higgins did in the play — turning the gentlewoman into a street urchin. In some accounts, Hart's spouse, Kitty Carlisle, assisted in the marathon lessons that enabled her not only to play the part but to make it one of the stage's most memorable performances.
Here's concert footage of Julie Andrews performing a number of that show and telling a small, funnier version of that story. It runs five minutes.