1881, Horatio Alger, From Canal Boy to President or The Boyhood and Manhood of James A. Garfield, ch. 25
[H]e acted as chief of staff to General Rosecranz, aiding his superior officer at a most critical point in the battle by advice which had an important influence in saving the day.
Maybe a strapping woodsman will come along and save the day.
Usage notes
Often suggestive of a rescue executed in a valiant or heroic manner, and sometimes used ironically to indicate that the rescue was not particularly heroic or that the situation was not particularly dire.