The story
Professional football games in the United States are most often played on Sundays, making Monday a likely day for fans to discuss and critique the performances of teams, in particular that of the quarterback who leads the offence on the field. However, there is evidence that the term actually derived in college football, which is usually played on Saturdays, in which case the use of Monday would also likely be on account of Sunday being the Christian sabbath and a traditional day of rest in the U.S., making it unlikely certain groups with a common interest in the game (such as co-workers) would meet before Monday.
Etymology from Wiktionary, CC BY-SA 4.0.