[UPDATE} It appears the best method is the credit card with double-sided tape. read about that approach in the comments. My problem was that the CD (likely the case for DVD disks as well) was physically stuck because of a clear plastic label placed over the playlist side of the CD. I didn't notice it when I inserted it, which increased the thickness of the CD beyond the tolerance of some aspect of the MacBook's eject mechanism. I fiddled around with it for quite a while, trying all the various solutions on the Internets, but none worked.

The slot has a felt dust remover that makes it hard to see what's happening inside. Finally I noticed a metal spring that acts as a kind of door in the middle of the slot. The spring moves up and down when you select eject, which allows the disk to pass.

I suppressed the spring from the top toward the bottom using the very tip of a fine-bladed knife and hit the eject button. A very thin-tipped flat screwdriver would probably work as well, but the business card trick did not hold it down. The drive tried to eject the disk repeatedly and finally I saw the tip of the disk emerge.

Over the last year, many other people have shared additional approaches on this thread, so read further if my method doesn't work for you.

If this happens to you, be patient, keep trying, and you'll get it out without wrecking the drive or spending a lot of money to have someone else remove it.