I've heard it came from an old advertizing campaign. Barbers put signs saying "Tomorrow, free shavings!", people saw them and took note to come back the next day for their free shaving.
And on the morrow, after getting their shave, they were of course asked to pay. "But," people would complain, "wasn't it free today?" And they were replied, "check the sign, it says tomorrow, not today!"
True or not, the story explains the saying. That idiom is used sarcastically to imply a promise will never be kept.