BALLS OUT

At maximum possible speed. Derived from operation of a mechanical governor on a steam engine, where a shaft spun two opposing balls. When maximum speed was set, the balls rotated in their greatest radius. Example: We're so late on delivering on the Hiphip Project we need to go balls out--so we'll start with an all-nighter. [ED. Any idea of the etymology of balls to the wall, which means essentially the same.]