Well, you hurry up, yes? I'm not going to poireauter 107 years old ! This expression of course means to wait a very long time. This is where the expression would come from.
As for leek or "leek", it should be noted that in the middle of the XIXe century, the expression was actually "plant your leek". It probably came from the phrase "stand still", which implies immobility, inactivity. Doing the leek means standing straight, motionless to wait a long time.
- Treasures of French expressions by Sylvie Weil. Belin, 2008.
- La Fin des haricots: And other mysteries of French expressions by Colette Guillemard. Omnia, 2009.