It's by Bob Rivers, from his album "Twisted Christmas". I've attached a link to their website, that has tons more of his Christmas tunes. Among my favorites: "I am Santa Claus" (a great little Ozzie parody) and "The Restroom Door Said 'Gentlemen'".
And I'll correct something I said earlier--I must have heard it in college, not high school, as the album was released in fall 1990, and I graduated high school in '88. (Unless, of course, the song was on the radio for a few years before the album was released.)