That fact that you can't call it the Jewish lobby is exactly the squeamishness I'm referring to. The Jewish lobby are not at all shy about saying that they support Israel because they are Jewish. There are of course some Jews who claim to hold the opposite opinion because they are Jewish, but it is clear that the economic and political influence of Jewish Americans is overall pro-Israeli and pro-war, most recently advocating for a proxy war with Russia in Syria.
Also comparing three terms on google trends suggests the left haven't been nearly active enough in promoting either concept:
https://www.google.com/trends/explore?q=Jewish%20lobby,milit...