Both legs

My mom used to use this, any ideas on its origins, other than my mom?

Talk the hind leg off a mule

Thanks

Not just your mom, not by a long shot. This expression was old when your mom was a teeny-bopper. If she ever was. SS

Well, it's not just the "hind legs off a donkey." This phrase is just one in a series. Here are some examples from This Dog'll Really Hunt: An Entertaining Texas Dictionary by Wallace O. Chariton:

Talk water into a boil at 20 paces.
Talk the hide off a longhorn bull.
Talk the hide off a gila monster.
Talk the legs off an iron stove.
Talk a wagon out of a ditch.
Talk the ears off a wooden Indian.

And from previous discussions:
Talk the bark off a tree.
Talk the hind leg off a donkey.
Talk the hind leg off an iron pot.

We're a bit more accomplished at this sort of thing here in Ireland. We 'talk the hind legs off a horse.'