I don't know if Jack Benny said it or not. But my mother, grandmother, aunts, and I have said it on more than one occasion.
You say it when you're feeling left out.
Let's say Gracie, Andy, and osso decide to have lunch somewhere together. I'm sitting right there. I say. "What am I? Chopped liver?"
Gracie, if you're gonna use the expression, that's the only way to say it. What am I? Chopped liver?
Although I'm sure that people in Noo Yawk use the expression, the derivation is definitely Jewish. Who else makes chopped liver.
If you're interested in more similar expressions, I suggest you check out this thread:
http://able2know.org/topic/10418-1