Yeah, the size would have to be pretty enormous in order to tip a card table.
I also had the idea of a robot that you place in the center of the table, and has two big arms (just like Chlorine) that fold down and rotate. It would look similar to a fan, and it would push the LEGO bricks in circles. Eventually, all the bricks would fall off due to centripetal force. Here's a picture:

I would have to build the arms longer than Chlorine's due to the fact that the arms would be reaching across the hypotenuse of the table rather than one side (they would each need to be 6 inches longer). Also, they would need to have more height when rotating on the table to avoid bricks just skipping over it.