You might not have an idea, but you sure nailed it on the head. I just looked it up a few minutes before originaly posting the question and that was the name. In fact you can actually find a few episodes on
YouTube if you want to refresh your memory.
My wife was watching an 80's movie, and one of the characters was lip syncing a song which sort of, kind of jogged some old memory of a show that used to do that, so I looked it up, and sure enough, Puttin' on the Hits was what I was thinking of.