Edit: She actually was not far off base. Historically they did tie the turkeys down.
A turkey shoot is an opportunity for an individual or a party to very easily take advantage of a situation.
The term likely originates from a method of hunting wild turkeys in which the hunter coming upon a flock, intentionally scatters them. Once the flock is scattered, the hunter sets up and waits, as the scattered flock will return to that point individually, making them easy targets.
A "turkey shoot" is also a shooting contest where frozen turkeys are awarded as prizes. The shoot is most commonly held, using shotguns aimed at paper targets about 25-35 yards away. Original turkey shoots, however, dating at least to the time of James Fenimore Cooper, were contests in which live turkeys were tied down in a pen and shot from 25-35 yards. If the turkey died, the shooter received it as a prize. This gave rise to the military term (see below). Another contest provided a caged turkey with a protective wall. Above the cage was a slot in which the turkey could raise its head. Single shot rifles were used and if the shooter was skilled and fast enough, the turkey was shot in the head rewarding the shooter it as his prize. Today, turkey shoots are still popular in rural America. The winner is chosen according to which target has a shot closest to its center cross-mark. This removes almost all luck from the contest, and allows every shooter an equal chance.
In military situations, a turkey shoot occurs when a group or team catch the enemy off-guard or out-gunned to the point of being unfair. Examples of famous military turkey shoots: