I was watching a History Channel program which suggested that the phrase "in a pinch" came about during the 1849 Gold Rush in the Western United States. It had to do with goods being exchanged for a "pinch" of gold dust in lieu of official coins or paper money (these being in very short supply). Merchants would hire clerks with large hands because they could "raise more in a pinch".
I have not been able to find the origin of this phrase, but feel that it surely must be older than this.
The word 'pinch' - from Old French 'pincier' - to mean what can be grasped between finger and thumb - has existed in English since the 14th century. The phrases at/on/in a pinch have existed since a century later.
