I don't know if you found the music already or not, but since I've been looking for the same music, and just found out the info, I'm posting the reply here.
The singer is Paula Cole
the song name is "It's my life"
It seems like she made several versions of the song for Mercury, and I belive the one you are looking for is an acoustic mix version.
Hope you come back here for this or found one already!
> Does anyone know the name of the song played in the Lincoln Mercury commercial that aired recently. The commercial is themed "Behind The Door" or "See what's behind the door".