I daresay that the majority of Israelis are not actively in favor of transfer as a policy - but usually the majority of a population is not consulted. According to an October 2001 Ma'ariv poll, 50% of Israelis were in favor of transferring the Palestinians out of the West Bank and Gaza. Since the poll is seven months old now, I assume the percentage today is considerably higher.
The opinion polls reflect various views, but there is no agreement on this issue, most especially HOW such an expulsion might be achieved. Israeli society is complex, and I don't pretend expertise about them. I think that they have more than one establishment, and unusually involved, well-educated and politicised population. Ethics matter to them, to an unusual degree, but that does not prevent extremism. Rmlew writes that "The elite in Israel is made up of leftist Ashkenazis." Yet note that the idea of transfer also has a pedigree on the side of left-wing Zionism, as well. Also, Ariel Sharon has been complaining all his life about the left-liberal Israeli establishment, and how they keep him down, and not allow him power. If only! While making all these complaints, he has gone from strength to strength. I don't like him, so that's my view. I wish someone had managed to keep him down.
Israel's alliance with the Phalangists in Lebanon, that was largely the work of my unfavorite person, Sharon. It is not accurate to say that they entered it because the had the same opponents - the Palestinians, Amal and the Hezbollah. Hezbollah wasn't founded at the time when Israel invaded Lebanon, it was a product of the occupation. Up until 1980, Israel had a good relationship with Amal, which represented a conservative Shia view, hostile to the PLO. (The type of view which one finds in the writings of Fouard Ajami.) But they swapped that for an alliance with Gemayel's forces. The lure was ideological (it can't have been tactical - the Maronite forces were as useless as tits on a bull.) The Kataeb (Phalangists) were left overs from 1936. The Lebanese Jews could tell you a thing or two about them.