Lyric discussion by big1002320 

Cover art for Shoehorn With Teeth lyrics by They Might Be Giants

It's political satire. The character is part of a larger demographic, probably working class conservatives (overly patriotic, fundamentalist, hive-minded and uneducated). Obviously, not all of this group of people are represented in this song, only the bible thumper fundmentalist types.
'Shoehorning' is a term with a potentially political meaning. According to Wikipedia, it is defined as "the act of coercing or pressuring an individual into a situation which does not leave enough room, either literally or figuratively." "The kind with teeth" - a human So, it is probably referring to someone who desires an authoritarian political leader.

My Interpretation