Perhaps the single most important thing to understand when trying to explain Israel's positions and behavior is what Israelis think is happening in the world around them. What are the sort of things they notice and take seriously, the things they think are important. I'm talking about impressions and perspectives, not necessarily strictly objective truth. Then again, strictly objective truth is hardly what informs anyone else, either. People act on what they perceive as true, not what is true, even when that can be determined.
So here are a number of stories Israelis notice these days - not all Israelis equally, but enough of them to effect the mainstream, I'd postulate.
Most (not all) Palestinians see the two state solution as a stepping stone to the no-Israel solution. Elder of Ziyon has some commentary on the poll here.
Ma'an News Agency, that's the PA news agency, tells that the Palestinians are furious that the Israelis intend to renovate the plaza in front of the Western Wall, because it's in conquered territory and abuts on the Haram a-Shariff. (And also the Temple Mount, but that's not mentioned).
General Amos Yadlin, the departing chief of Military Intelligence, warns that the next war with the Iranian backed alliance will see Tel Aviv as its main battle ground. I suppose you might reassure yourself that if Israel retreats from the Western Wall and makes nice to the Palestinians they'll give up on the practicalities of their dream to have no Israel, but I don't see how that effects the Iranians and their local allies; if one lives in Tel Aviv or any other town with lots of Jewish civilians, this may well be a serious consideration as one forms political positions.
In an ongoing story, the PA leadership seems to be preparing the ground for abandoning the possibility of reaching a peace agreement with Israel and using the UN to achieve statehood without compromising with Israel on things the Palestinians don't wish to compromise on. As I've noted but haven't fully fleshed out, my personal position is that Israel could use such a Palestinian ploy to achieve the opposite effect, of leaving the Palestinians with less leverage to achieve what Israel can't give. But that's just me. Clearly, the Palestinian leadership doesn't see it that way, and their intention is hostile to Israel.
Update:Ben Smith of Politico, wandering around Israel talking to folks, tries to figure out what Israelis are thinking these days. It's interesting. (h/t Thom).