If you had more time you could buy a song from iTunes through the United shopping portal.
Why do you need 1 mile so quickly? If it's to keep miles active, you can do that by redeeming them for a magazine subscription. Some can be had for around 300-500 miles. Blowing a few hundred miles is a lot better than losing thousands.
Actually come to think of it, I think United just launched some sort of digital content shopping mall where you can redeem 100 miles for a song. Maybe you could go that route.