The third and fourth verse split a wandering verse. The version I know goes like this:

A horse and a flea and three blind mice
Sat on a curbstone shooting dice.
The horse he slipped and fell on the flea.
"Oops" said the flea, "There's a horse on me."

The point is that in the dice game called "Horse," players who loses a round are said to have a horse on them. So I'd guess the ? word is either "there's" or "that's," and "the" might be "a."