Green’s Dictionary of Slang

(US) a person who criticizes with the benefit of hindsight.

1931		Arcadia (CA) Trib. 30 Oct. 5/4: But he found a Roman army there before him, with another close on his trail. He was licked, and he knew it. He didn’t spend any time in vain regrets. Spartacus was never a Sunday morning quarterback.
1931		N.Y. Times 5 Dec. 22: Barry Wood, Harvard’s all-America quarterback, mounted the ramparts in the role of a defender today [...] The answer to overemphasis was to be found not on the field, but in the stands, where sit what Wood called ‘the Monday morning quarterbacks.’.
1931		Sheboygan (WI) Press 17 Nov. 4/3: Are you one of those Saturday night and Sunday morning quarterbacks who knows what they ‘should have’ done to win the game?
1958		R. Chandler Playback 101: Common sense is the Monday morning quarterback who could have won the ball game if he had been on the team.
1978		P. Theroux Picture Palace 32: I know all old people are Monday morning quarterbacks.