Out on a Limb

A limb, in the sense of a tree branch, is a genuinely risky place to be: climb far enough out along one and it can bend, crack, or simply snap under your weight, especially if someone below decides to "shake it or saw it off." The figurative use is American, appearing at the end of the 19th century. The earliest confirmed citation recognised by the Oxford English Dictionary is from 1897, though an earlier, disputed example from the Steubenville Daily Herald in October 1895 uses almost identical imagery, discussing cutting off a political rival's supporters: "if we get the 14 votes of Hamilton we've got 'em out on a limb... shake it or saw it off."