I did a little more digging.
George Root was well known as a fast and prolific composer of catchy songs. He was an associate of Lowell Mason, who was an advocate and a practitioner of the art of memorable, singable tunes in the hymn genre.
The accounts I have read claim Root wrote the song in a day or so to fill the need for an upcoming rally. It seems plausible, given his other work, and I have seen no indications of any claims that he lifted the tune from an existing source.
His tune Tramp, Tramp, Tramp is another example of one that has become so universally known that it might be mistaken for trad. Following its career as a war song, it was picked up by Irish nationalists, union organizers, and Sunday School leaders (Jesus Loves The Little Children).
-Glenn