We did it! Hatsune Miku's popularity finally rose up enough to actually perform on David Letterman last night. While I didn't watch it live, since I don't particularly enjoy David Letterman, I didn't get to see Letterman's intro for Miku, which also could have been somewhat comica. However, the official YouTube video does let you watch the entire performance, as well as Letterman's reaction to it afterwards.
Hatsune Miku performed 'Sharing the World' which isn't necessarily one of her more known songs, but it does have a lot of English lyrics in it, so I guess it makes sense they'd choose that one to appeal more to the American audience who isn't familiar with her.
You can check out the video right here:
You can certainly tell that Letterman isn't really sure what to make of the performance after, as he's awkwardly waving to Miku, and then stating, "It's like being on Willie Nelson's bus."