Update: The audio clip used in that commercial might not be Whitman after all. From the inbox:
The Walt Whitman recording that is being used by the Levi's commercial that you posted on the 28th is actually not Whitman, and is now considered by most audio archivists to be a hoax.
More information about this most interesting recording can be found in Vol. X, No. 3 of Allen Koenigsberg's Antique Phonograph Monthly magazine from 1992, pages 9-11.
Among things pointed out, one is that the speech on the soundtrack ends with the quote, "Freedom Law and Love," whereas the original printed version of the poem ends with "Chair'd in the adamant of Time."
Koenigsberg also points out that Whitman's last years were chronicled on a daily basis by his personal secretary, and being wheelchair-bound, such a visit for Whitman would have been difficult, unprecedented, and undoubtedly noted.
I remember when that happened to me. I'd been working for 12 years, and then the part in "Easy Rider" changed my life. Very few people have ever had the experience where they sit back and say, "I am a movie star." I knew it at the first showing of "Easy Rider" at the Cannes Film Festival by how the audience reacted to the movie. A lot of people would say, "I know I'm a movie star, but, oh, I wonder what's going to happen..." I knew it then: I was a movie star. And it was great.