I heard this song one time a couple of months ago on my Sirius
satellite radio. I guess I wasn't too impressed with it at the time,
so I didn't take note of the identifying information, but three days
later it popped into my head and has been stuck ever since. I'm dying
to know the name of the band/artist and the title of the song! The
lead singer was a male who sounded like Iggy Pop but spoke-sang most
of the lyrics like Bob Dylan does. His delivery was very expressive.
The lyrics I know for sure are one of the verses:

"Baby, move on. Baby, MOVE on. Sweet, sweet, sweet, sweet baby move
ON!" [I'm totally guessing on the punctuation.]
The next line was similar, with the words "I'm gone", or something
close to that, replacing "move on".
My best recollection of the chorus is: "I'm [something] you. (repeated
by backup singer: I'm [something] you.) And it hurts me, too.
(repeated by backup singer: And it hurts me, too.) And I'm turnin'[?],
turnin', turnin' you away now."

The song was in a major key and 4/4 time, if that helps. I've tried a
bunch of different combinations of the lyrics in google, but
unfortunately, they're pretty popular words as lyrics go. One other
thing that may be of assistance to you, if you're familiar with
Sirius, is that I'm pretty sure I heard it on either channels Disorder
24, Underground Garage 25, or Left of Center 26. However, that means
the song isn't necessarily a recent one, seeing as how those channels
play music from all decades, and the song was just a simple, timeless
rock tune. I leave my obscure music sanity in your hands.