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They Might Be Giants – Shoehorn With Teeth Lyrics 8 years ago
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.

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