Israel is starting to hint that they have full intent to take down Hamas with this war in Gaza (though this has been pretty obvious for a few days now). Their confidence that they can do so is surprisingly high, as well--Israeli officials are calling Hamas "crippled" in a few ways: its physical governance infrastructure is ruined (parliament building, police buildings, etc), its leadership is dead or in hiding (having abandoned its population), and its popularity is going to drop.
Though the popularity of Hamas is currently rather high, the Israelis think it will go down significantly in the next few weeks as Palestinians wonder whether a militant anti-Israel stance is one that is going to serve them well in the future. In particular, if Hamas is unable to provide governance, order, medical supplies, etc after the war ends, then their support will erode. Pre-war, Fatah already had an edge in Gaza polls. When the Palestinians have elections, probably in April 2009, Fatah will probably have quite the edge, even in Gaza. And if it does, and if Kadima can hold on in Israel, then the whole situation in Palestine looks a lot different. Israel will probably do what it can to enforce Fatah's right to govern in Gaza Strip, and help clean the strip up before working on serious two-state talks.
Such confidence is strange, coming from an Israel that lost a 2006 war in Lebanon due to overconfidence and poorly-defined campaign goals. Israel had been showing serious conservatism in its war goals early on: the air campaign was aimed at reducing rocket attacks, not even eliminating them. While Israel is not saying that they have changed their goals to the toppling of Hamas, they are certainly saying that it's likely that they will, and that they're quite happy for it. This means one of two things:
1) Israel's government did not learn a lesson from its tough defeat, even though I was able to graft that lesson from my seat in Cambridge, or,
2) Israel is actually well and truly crushing Hamas' governance and combat capabilities.
Occam's Razor says it's probably the latter.
Despite confidence, Israel remains conservative. They have not given in to goading and luring on the part of Hamas to enter Gaza City or other urban areas for street fighting. They have kept their total military casualties to one, suffered on the first night of entry. Israel's targets have been picked with deliberate caution, as well: Palestinian medical authorities have reported only 16 children dead, despite a strong incentive to over-report. Hamas has claimed that half of the over-500 killed in Gaza are civilians, but there is a strong incentive to over-report here, as well: Hamas loses face by reporting its own fighters killed, and gains support by claiming that Israel has killed civilians. Given how informally one can join the Hamas paramilitary, it will be impossible for these figures to ever be confirmed beyond academic estimates.
So things seem to be going well for Israel so far. They have a lot of work to do, and in particular, Israel must keep up strong diplomacy with Jordan, Egypt, and Lebanon, in order to keep its free military reign in Gaza. But such support should have wavered days ago if it was going to. Israel appears to have a serious shot at crippling Hamas for good and, despite the cries of many protesters to the contrary, contribute to long-term peace in the Middle East.