The actual use of the text to the Preamble to the U.S. Constitution works as a sort of song within a song in this cartoon. As an entity unto itself, this short tune lasts about forty seconds and is heard twice (beginning at 0:45 and 1:55 in the video). The construction of the thing is quite beautiful.
There are 24 bars total, the first sixteen with a pattern of one chord and mostly one line of text over two bars of music. It looks like this:
We the people (I)
In order to form a more perfect union (IV)
Establish justice, ensure domestic tranquility (I to V)
Provide for the common defense (I)
Promote the general welfare and (IV)
Secure the blessings of liberty (I)
To ourselves and our posterity (V)
With only a few lines of text left, the tune now takes a turn. The melody is entirely new and the chords no longer hold for two bars each.
Previously sticking to a limited tessitura with no note above G, the melodic line here skips up to the octave right when the chord changes for the first time without waiting for two bars. Text spills over into a four-bar phrase, and then a second one (broken in half) that manages a strong cadence with a real sense of conclusion that, despite the tune's real brevity, doesn't seem at all abrupt.