"call the ball" is what a naval aviator does when he's landing on an aircraft carrier. When the control tower tells the pilot to call the ball, they are turning over control of the landing procedure to him for a bit, so it gets used to mean "it's your call" or similar.
And I was trying to remember the Bush story about it, so I googled and got it:
There is a visual aid used on carriers to let pilots know if they are on the proper glide slope to land on the deck. The part that moves up and down depending on how you're doing on the glide slope looks like a ball or "meat ball". The fact that you have a visual on the approach aid dictates a call to the controller on the ship.
The President's recent approach to the aircraft carrier Abraham Lincoln resulted in the following: In this case the standard response from the pilot of plane carrying the President would have been "Lincoln, Navy One, 12,500 lbs, Roger Ball" meaning I have the ball in sight and am on glide path (for a safe landing -- the weight is given for setting the correct braking tension of the arresting gear cables).
The President's recent approach to the aircraft carrier Abraham Lincoln resulted in the following: "Navy One" was on final approach for trap aboard CVN ABRAHAM LINCOLN... the President, making the radio call, said:
"Lincoln, Navy One, 12,500 lbs, I have the balls"
His call brought down the house in wild cheers.