I have open Johann Blumbenbach’s A Short System of Comparative Anatomy, in the 1807 English translation by William Lawrence. The full text is on Google Books.
In a footnote to page 24, where Blumenbach described the various horns and antlers of the group known as the Pecora, Blumenbach describes the jackalope!
I have collected about twenty instances, from the middle of the 16th century downwards, in which horned hares are said to have been found, with small branches like those of the roebuck, both in different parts of Europe, and in the East Indies. Were this fact ascertained, it would furnish another striking point in which these animals resemble the pecora. The fact is suspicious, because I have not yet been sufficiently satisfied of a single instance in which the horns were on the hare's head, although every trouble has been taken to procure information; and they appear in the drawings, which I posses [sic], by far too large for a hare.
It seems likely that the source of this idea was the muntjac, or other small cervids. Still, it’s not hard to imagine Americans heading west, thinking that some of the large jackrabbits might turn out to be antelope-like in more ways than one.