This is the key, IMO:
Judging from the administration's responses thus far, it appears far more likely that what the president would like to see laid low is not the Netanyahu government's head, but rather the part that often verbally functions as its butt end - specifically Foreign Minister Avigdor Lieberman's Yisrael Beiteinu party and Interior Minister Eli Yishai's Shas.
In the current Israeli political constellation, these two men, and these two parties - a volatile alliance of ultra-secular Russian-born immigrants and ultra-Orthodox sabras with roots in the Muslim world and the Mediterranean - are the effective veto both to the peace process as a whole and to a settlement freeze of any substance.
They represent a total of 26 of the 61 Knesset seats needed for a Netanyahu majority. More crucially, they are the primary roadblock to the entry of the centrist Kadima party, which at 28 seats is larger even than Netanyahu's ruling Likud.
Obama, whose math and history skills are as good as anyone's, knows both that Israeli government concessions are a near-monopoly of the center-right Likud. It is thus reasonable to assume that the president would like to see a Netanyahu-led coalition anchored by Kadima and Labor, whose 68-seat cushion could allow for the inevitable resignations of "rebel" Likud backbenchers.
If Sharon can break from Likud and form Kadima, Netanyahu can replace Shas and Yisrael Beiteinu with Kadima
et al (I read that Jewish Home was pushing for this too, they're small but almost 3% is still sizable in Israeli politics). After all, it
is the land of miracles. ;-)
PB