My ex went on a cross-country drive a few years ago, and he said it was really striking how ever local newspaper he came across inevitably carried some story about Israel/Palestine. Our 51 state, he calls it.
So I think popular support for Israel is a combination of things: racism against brown-skinned people (Arabs), the belief that Arabs are terrorists, the perceived continuity between OT and NT (the fear of Islam), the barely concealed admiration for the thuggish conduct of the Israelis, and the identification with the troubles of a white settler state. ___________________________________
There's also a heavy effect of Bible-based churches' encouraging their congregations to read the Bible. Few people get much beyond Genesis and Exodus (Leviticus will bog you down every time!), but they end up pretty marinated in the notion of God's chosen people and the promised land. The more fundamentalist churches go on to preaching about the Apocalypse. Since the 70s and 80s, there's been a popularization of the notion that the Temple at Jerusalem will have to be rebuilt, and all the Jews convert to Christianity prior to Armageddon. While I'm not sure that many people consciously, rationally think about all this, I do think that there is a religious compartment of the mind where they think they totally believe. So if you don't follow foreign affairs very closely, have these religious emotions in your mind, and hear the odd snippet of a political figure's speech about the only democracy in the Middle East, you likely end up thinking that the U.S. should support Israel.