Do not thaw on the counter. Thawing at room temperature increases the risk of bacteria growth.
At room temperature, bacteria on the turkey can grow rapidly when the outside portion of the bird begins to thaw. These bacteria can multiply to dangerously high levels producing toxins that cooking may not destroy.
Leftovers should be stored in the refrigerator within two hours after cooking is completed. Why just two hours? Because bacteria that cause food poisoning can multiply to undesirable levels on perishable foods left at room temperature for longer than that.