Most uses of this phrase are referencing actor Gene Wilder's portrayal of Willy Wonka in the 1971 movie "Willy Wonka & the Chocolate Factory," where Wonka informs Charlie he has lost the contest because he drank the burp soda, a breach in the contract he signed. "You lose! Good day, SIR!" Wonka screams at Charlie before turning back to his desk.
Linking to an animated gif of the scene with the audio intact is a popular way to assert you are done with an argument on the internet.
Jeff: GOOD DAY SIR!
DMS: Good day.