"Tom Hauer writes:
I've seen the expression "ballin' the jack" in several folk songs and one novel. It seems to mean "expeditiously" or "with great haste," though one phrase led me to believe it meant "to dance aggressively." Are any of these definitions accurate?
They are all accurate, if you add "to do something" to your adverbial definitions.

The phrase ball the jack was popularized in 1913 by a ragtime song by Jim Burris and Chris Smith called "Ballin' the Jack." This well-known song introduced a dance step of the same name that was the subject of the song, so one sense of ball the jack was 'to perform (the dance step introduced in the song)'.

The usual sense of the expression, though, is 'to go fast; make haste', and this is often used in reference to railroad trains. This train-related use seems not to be the origin, however; jack 'a railroad locomotive' isn't found outside this phrase until later. (The phrase is verbal, which is why I said that it doesn't mean 'with great haste', but rather 'to do something with great haste'.) A slightly different sense is 'to work hard and efficiently'.

The ragtime song was published in 1913, and the phrase is not attested earlier. It is unknown whether the song actually coined the phrase or merely popularized an already existing one. Both the 'go fast' and the 'work hard' senses were common by the end of the 1910s."