> Now I'm wondering, because now that I think about it, "like George Washington" and "like Monopoly" have the same number of syllables. Maybe Sam's reindeer played Connect Four or Parcheesi.

No, although I'm not 100% sure that we sang "Monopoly" there. But probably we did.

You make a good observation, but the arrangement of syllable stresses is more important for rhythm than the raw number. You can almost always get away with including or omitting an unstressed syllable at the beginning of a line of verse, for example, and you can do it at the end, too, as long as rhyming lines match up.

Now that I'm on this train of thought, maybe that's why "like George Washington" rings so horribly in my ear. In normal, spoken English, "George Washington" begins with a stressed syllable (followed immediately by another, which is not conducive to verse). In the song, "George" is artificially de-stressed. "Monopoly," on the other hand, normally starts with an unstressed syllable anyway.

"Columbus," despite having fewer syllables, still lines up with respect to where the stresses are.

While googling, I ran across a page that listed the echo as "like the Presidents." My childhood memories won't let me accept that version as "correct" either, and even that page admitted that both "like Columbus" and "like George Washington" were more common. But "like the Presidents" does fit the rhythm quite nicely.