Another way of saying, "All Day Sex (after the kids go to school till 3:00 when they get out)". It's treated like a Mexican holiday, with the Tequila shots, etc. between bouts. Also, sometimes means an extra long time having a hard-on without ejaculation, or an all day hard-on.
Hey, you wanna have Fat Tuesday with me tomorrow? (doesn't matter what day of the week it is). Or: Damn, I was Fat Tuesday after I saw you in that outfit this morning.