In order for it to feel more authentic, Beck filled out Song Reader
with a number of song fragments, melodies, and fictional album collections and song titles. "A-M-E-R-I-C-A" is listed as part of a series of "Late Patriotic Song Successes!", all songs about soldiers and war and the like (a popular sheet music genre in the early 1900s.)
The idea of "Late Patriotic Song Successes" came from the back of a piece of sheet music that you can see here
. Beck's page has 6 fragments, and many of them can be sourced to that page.
One of the songs listed there is called "A-M-E-R-I-C-A (Means I Love You, My Yankee Land)."
Beck's lyric and melody are seemingly unique, it's just the title he borrowed.
Beck's fragment is credited to a "C.A. Hoffman," which is far as I can tell is just a made-up pseudonym.