Not that easy to get on Letterman, unfortunately. I just think they haven't had a breakout song yet. Kinda surprised the label never ran with Tallulah as that's probably the closest they've gotten even if it's not their normal sound.
I think a big reason they're better live is Genevieve has become a lot better singer & performer since they started out. I think they also really excel with just her & Marc (the guitarist) since it allows her more freedom to just let loose on stage. I haven't been super-impressed with the rest of the various band members they've went through.
A couple videos some other people took
The video I took is clipped beyond repair, but here's one of the pics I took.
A couple other things to mention... so weird to see Genevieve walking around with a hat/
glasses on before/after the show and not be recognized at all, even by fans of her band. Definitely almost had a "secret identity" thing going on. She's a cute girl but doesn't stand out at all in a bar in a college town until she gets on stage and starts singing... then she completely commanded the room. You didn't see people talking and ignoring the music or walking out once the show started like you might in another venue. Everyone was completely into it once she started singing, whether they were big fans or just showed up because "they heard they are really good".
Also, I'm not really familiar with all the different versions of "Big Yellow Taxi", but the COT's cover was as good as my idealized memory of the song. It was basically a perfect blend of the original Joni Mitchell version and the Amy Grant/Counting Crows covers.