Give up the Old City/Har Habayit?

Most Israelis will sacrifice for peace but are against giving up the Old City of Jerusalem and the Temple Mount.
This is a very encouraging poll that indicates there is still a pintele yid in most Jews in israel, even the most secular of them. This pintele yid tells them that there are red lines and not everything is negotiable. Why should the Palestinians have such strong red lines that they can say no unless we get temple Mount and right of return and hot pizza every Wednesday (or whatever they want) and not have to give up on anything, while we have to be willing to talk about anything with no red lines. This article shows that we jews also have red lines.
Last night at our daf yomi siyum we got into a discussion (don't ask how..I do not remember other than last nights daf discussed a non-kohen goign into the kodesh kodoshim to do repairs and remove impurity) about negotiating Har Habayit with the Palestinians. One person had revolutionary idea suggesting that our problem has been until now that we, the religious public, has always been on the outside of the negotiations. We never took the negotiating of peace into our own hands, rather we always relied on the secular parties to negotiate on Israel's behalf, always relying on the hope that said leaders would stay within certain redlines that were acceptable by us. Ariel Sharon proved that hope to be false. We can no longer rely on such leaders to negotiate according to what we want. Sharon gave away Gush katif while an extremely large public stood on the side with the ability to do nothing (protesting was like screaming into a paper bag - nobody listened, nobody cared). In the future, the argument was presented, everything will be negotiated. You can be sure that the next PM, be it Olmert, or Netanyahu or anybody else from the not-religious political parties will reopen the negotiations and you can be sure a lot more will be offered than ever before. If we know in advance that they will negotiate Har Habayit (because that is upon what negotiations collapsed between Arafat and Barak - everything else was supposedly worked out), we should be involved and establish red lines in advance that we would settle for half of Har Habayit (because, he argues, if we do not than we will lose the whole thing). It might even be prudent to set up a political party with this as its platform (while Manhigut Yehudit puts Har Habayit in its program, MY is not a political party. Rather it is an entity within the Likud and therefore beholden to the Likud's lines to a major extent. the little power MY holds precludes their being anything other than a marginal voice on these issues).
Let me tell you this guy got an earful. Everybody was screaming at him that we also have top have red lines and why should we offer half, etc.. The above article shows that most Israelis would reject such a negotiating stance and therefore our red line should not be half of Har habayit, but we want the whole thing.