It is my opinion that this song is a political allegory to the futility of the two-party system in America. The pusher robot represents the Republican Party, and the shover robot represents the Democratic Party. The basis for this belief lies in the first two stanzas after the first chorus. The pusher robot "shoves around the blind people." This is very Republican; the right wing tends to not be concerned with the welfare of those who cannot work and contribute to society. However, the other robot in the song, the shover robot, "pushes bread down their throats." This is symbolic of the Democrats' concern with welfare, to the point of actually hurting the people they are supposed to help.
Each robot claims that they are supposed to protect the humans of Earth. However, they never deign to explain exactly what they need protecting from; the humans are only told that there is "a terrible power." Also, the shover and pusher robots each believe that the protection is for the good of the people, even if they do not understand it.
As a final allegory, each robot believes that the other robot cannot protect Earth. With claims of "I am superior" and "I am better than the shover robot," they neglect to tell people that they do the same thing. If you shove something, the result is exactly the same as if you push it. The author of the song is trying to say that as long as we allow the space robots to run our lives, we will find ourselves lying crumpled at the bottom of the proverbial stairs.