If it's your first time getting music, he won't ask for requests. He'll just play you a song and give it to you. After that you can make requests and such again. This is how it worked in City Folk at least, and I think Wild World, too. It helps so that people who don't know what K.K.'s deal is won't request some useless song, get nothing worthwhile out of it, and wander off without knowing you can get music.
Which actually happened to me way back when the first game came out.