The "earliest appearance in print" is simply the earliest date that someone working for Oxford or Merriam has noticed, and a fifteen or twenty year discrepancy isn't too remarkable.

I quickly found the following in a newspaper database, eleven years before the Civil War:

"Christian Freeman and Family Visitor" (Boston, Mass.), Oct. 11, 1850:

"Their manner of drill, and their patriotic explosion of gunfire reminded us of the good old military times of our boyhood. The boys ran an opposition to the company in the firing line, by the burning of powder in a hole in a blacksmith's anvil....It was quite a fete."

In any case, the song itself is so evidently a Civil War product ("We'll be ground beneath the tyrant's heel,/ For our demands of justice") that the question of just when a single word or phrase first appeared in it seems like a quibble.

A less likely point of origin would be some long forgotten, postwar stage performance. But there's no evidence for that, and apparently nothing in the song we have casts doubt on its existence during the Civil War - if only, perhaps, in Bells, Texas.