As so many point out here, Bush (last time around) did not get that many Jewish votes. Yet he won. So much for the 'power' of the 'Israeli Lobby' (so-called.) There is no group in America that does not advocate for it's cause. From the Catholic League to CAIR to Cuban-Americans, it's what's done. And by the way American Jews are not a monolith. On the Left you have the ADL, which supported Gore, on the Right you have Americans for a Safe Israel, which supported Bush. The Forward is Liberal, The Jewish Press is Conservative.
In addtion, it is absurd to believe American support for Israel is only the result of pressure or lobbying. It has much more to do with shared values, etc.
Americans are aware, more than ever (see the Gallup poll just out yesterday) that many Muslims do not like America, do not like Bush, think Arabs did not perpetrate 9-11 (LOL) but that Israelis love America.
You are being entirely too modest about your Israeli Lobby.
There is absolutely no other advocate group in this country that reaps such monetary and political benefits.
As you mentioned, this has been achieved by trying to control both sides of the so-called Left-Right spectrum.