'Looks like it was originally performed (in the counter-point style) by Johnny Long in 1940...

"A young bandleader from North Carolina, Johnny Long, had his entire band sing a parody of the sentimental tune in an up-tempo rendition that became very popular."

There are MP3's on the web, so just search for "Johnny Long" and "MP3". (I can't right now; I'm at work!)