The point of the song is to essentially tell children that a bit of a song whilst cleaning up can make the cleaning go a lot smoother, and with a lot less complaints. Of course, the song also insinuates that you will have all your little forest friends to help you with the dishes, which, I can tell you from experience, is completely false. You are all by yourself in the cleaning up. But, I will admit that listening to music or putting on a movie as background noise while you work is actually very effective. It still takes two hours to clean out the closet, but it is easier to clean when Andy Dufresne is toiling away in prison and making friends with Morgan Freeman right next to you.
The concept is the same, even it is less 'cleaning up' and more of a 'packing up your entire life into boxes that definitely fit all this stuff in here on the way back down so where did all this extra crap come from anyway?' type of thing.
Therefore, I would suggest putting off the packing up of the iPod speakers or the television away for as long as possible. Keeping the iPod on relatively upbeat songs will help, though if your neighbors or roommates are also listening to music, various genres can sometimes clash a bit. This is fine, and at least you aren't alone with your thoughts when you are trying to figure out just how things will fit together in their boxes, and then in your car.
A movie or music is definitely a welcome distraction from the tedium of cleaning. And more often than not, 'packing' turns into 'cleaning' very quickly.
Movies certainly believe this about themselves. Especially Disney. Enchanted, Mary Poppins, Snow White, Cinderella and quite a few others have either a 'moving' scene or at the very least a 'clean up' scene, and all of them utilize song and dance and sometimes animals to make it more appealing. Because of this, I believe, I now find it impossible to even attempt to clean or move without some kind of aural or visual stimulation.
It works especially well if in the movie the characters are cleaning up as well. Or, even better, if their situation is about a million times worse than yours. You can enjoy the movie, clean up, and be very glad that all you have to do is figure out how to make your boxes defy all the laws of physics in order to pack everything up--it's easier than trying to save the world or escape from prison or crazy government agents, or dealing with any action move plot ever.