As already suggested, buy the refillable mug. The other thing to keep in mind is the time of day. I have yet to run into huge crowds at the POP food court. But, I tend to get there pretty early. By about 7:45 or so it's a zoo!!
Refillable mug is the only way to go, but there can still be lines at the coffee machines - we were there in Jan and always lines by 9am. Depends how irritible you are in the am before you have your coffee how long they will feel