I’ve never heard your phrase before, but in aviation we have a vaguely similar phrase, “balls to the wall”, which means using maximum power.
The accepted origin of that phrase is that the throttles and other various levers used to control the engine(s) used to be 6-8" tall steel stalks topped with 3/4" or so bakelite balls for a better grip, usually with engraved numbers to designate which engine they applied to, and often of differing shape or color depending on which engine funtion they controlled.
A WW-II era airplane had between 3 and 5 such levers per engine, which made for a whole mob o’ knobs on a multi-engined airplane like B17.
For max power, they were all pushed as far forwards as they’d go, towards the firewall that separates the cockpit from the single engine in the nose of smaller airplanes.
So when you need max power, grab all the balls and shove 'em up to the wall.
Perhaps your phrase is indirectly related, although at this late hour I’m having a hard time coming up with a connection.