The Monday before Lent, spent in dissipation. (German, der blaue Montag.) It is said that dissipation gives everything a blue tinge. Hence “blue” means tipsy. (See Blue Devils .)
Drink till all is blue. Cracking bottles till all is blue.
Fraser's Magazine, xvii. (1838).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Blue Monday from Fact Monster: