Anshel Pfeffer, a correspondent for the Israeli newspaper Haaretz, explains that there are three schools of thought among American Jews:
1) “Pavolovian flag-wavers” — “There are large number of Pavlovian flag-wavers, good and innocent Zionists and Jews who see only the trauma inflicted on the people of Sderot, Ashkelon and other parts of the country’s south-west, and instinctively position themselves behind the IDF, often saying that the government should have allowed it to go in further and strike harder.”

2) “Radical left” — “a somewhat smaller but highly vocal group belonging usually to the more radical left, and even fewer to the anti-Israel Neturei Karta sect, who feel compelled to atone for Israel’s manifold sins and join its enemies in the demonstrations and sign petitions accusing the Zionist entity of war crimes.”
3) The Conflicted & Ambivalent — “There is, though, a third stream of Jews – perhaps not the widest one, but I believe quite significant – who have more complex and uncomfortable feelings on the matter. They care deeply for Israel and understand even why its government felt compelled to launch the devastating Operation Cast Lead, but they are extremely disturbed and hurt by the level of civilian deaths and destruction that almost seems part and parcel of the action. Surely, they say, there must, there has to be another way of doing this. And they live with those doubts, often unexpressed, even among families and close friends because the worst thing they find is that others around them don’t seem to discern between the different nuances, and can’t find in themselves compassion for the dead and wounded on the other side.”
J-Street, a progressive alternative to AIPAC, has associated with this third group — and been called “anti-Israel” as a result. Mark Silk summarizes the J-Street controversy here.