As much as I wish this song were a dig on Obama, it's unfortunately not. I know this for a fact because Petrucci said, himself, that the song is about left vs. right in America. My interpretation of "backs of angels" is that we, as citizens, elect politicians with the hope that they're going to solve all of our problems, but they're not "really" angels, they're just humans who are greedy and manipulate the system for power instead of helping us or doing what's best for us.
The "days are numbered" part, to me, means that OUR days are numbered because this system can't keep continuing or our society will crumble. We're being led, "like lambs to the slaughter."