Let's start with the Palestinians, where a two-state solution meets the most opposition. From Haaretz's report:
"In another measure of the Palestinian mood, an opinion poll commissioned by the group The Israel Project, which dispenses information to journalists and others about Israel and the Middle East, showed that about 65 percent of Palestinians polled said they thought now was the time for diplomatic contacts, while 30 percent saw the current period as the time for violent resistance. On the other hand, only 34 percent favored a two-state solution involving a Palestinian state alongside a Jewish state. Furthermore, 66 percent favored a two-state solution as only a first step to be followed by a Palestinian state replacing Israel."
Lovely. They want to talk to us so they can eventually bring about our destruction? That's certainly how it seems. It is hard to read such a poll and stay an Israeli peacenik.
Israelis aren't that crazy about a two-state solution, either, but they are much more open to it than Palestinians, according to the Israeli Democracy Institute's June Peace Index poll:
"This month, we checked the extent to which the Jewish public is currently prepared for an evacuation of the territories. It emerges that the critical question concerns the “terms of the deal.” If one talks about a permanent peace agreement in return for evacuating all of the territories, only 25% of Jewish respondents express support. When one offers those who oppose a deal on such terms the possibility of leaving the large settlement blocs in Israel’s hands, the rate of support rises considerably to half of the Jewish public. If those who also oppose this formula are offered two more “benefits”—Palestinian recognition of Israel as the state of the Jewish people and a declaration of the end of the conflict—the rate of support for the whole package rises to 62%."So, most Palestinians only agree to a two-state solution if it will lead to a one-state solution, while most Israelis only agree to a two-state solution if all their demands are met, though the Israeli side isn't as extreme as the Palestinians - after all, while I don't agree that we should demand that Palestinians recognize Israel as a Jewish State (it is a Jewish State and will continue to be - we don't need their approval for this), I don't see it as a crazy demand.
A note to those who read the Peace Index's data file: I read it and thought we're in big trouble. At first glance, it seemed like a vast majority of Israelis opposed a peace deal, even with recognition of a Jewish state. The data file omits the very important fact, which only appears in the more detailed report, that the second question (where settlement blocs remained in Israel) was only asked of those who opposed a full withdrawal, and the third question (with recognition of Israel as a Jewish State) was only asked of those who opposed withdrawal while keeping settlement blocs.