"There seems to be no doubt of my election as V[ice] Pres[iden]t. It will have at least one advantage, that of permitting me to devote more of my time to my private affairs." [John C. Calhoun, letter to wife, Nov. 12, 1824]
"A lame duck is a man who cannot pay his differences, and is said to waddle off." [Thomas Love Peacock, "Gryll Grange," 1861]
Sometimes also in naval use for "an old, slow ship." Modern sense of "public official serving out term after an election" is recorded by 1878 in Amer.Eng., from an anecdote published in that year of President Lincoln, who is alleged to have said, "[A] senator or representative out of business is a sort of lame duck. He has to be provided for."