This is a song that my brother, mother, and I used to love listening to on the Dr. Demento show a few decades ago.
I don't know why I was thinking of this - just one of those memories that popped up uninvited. I asked whether the Internet had a copy, and the answer was "yes".
The song is by Mark Johnathan Davis A.K.A. Richard Cheese, who now makes a living (with his band, "Lounge Against the Machine") "swankifying" popular songs (imagine Dean Martin covering Nirvana)
His voice is uncannily similar to the guy from Barenaked Ladies