In Israel, it was usually referred to as "the fence." During the late 2002/early 2003 Israeli election campaign of Likud/Sharon vs. Labor/Mitzna, one joke making the rounds in political circles was that "the fence would win in a landslide," since it registered significantly higher approval from the public than either of the major candidates.
It should also be recalled that 35 years of occupation, settlements, etc. went by in the West Bank with no wall/fence/etc. Massive suicide bombing was what prompted it to be built, against the prevailing will among the right-wing and security establishments in Israel (it was originally an idea associated with the left, usually in tandem with unilateral withdrawal from settlements). Certainly the settlers detested the idea, since they feared that they would be the ones being cut off. Sharon OKed it only because it was too broadly popular with the electorate to resist any longer. It was only at that point that the settlers' influence kicked in and hijacked it (at least in part) to further their grip on various parts of the West Bank.
