By tonight, the governing party should have a new leader. After a painful summer limping along with an unpopular prime minister - who never came close to matching the popularity of his predecessor - the party will today have the leadership contest and the fresh start it has yearned for.

No, that's not a prediction of the imminent fate of Gordon Brown and Labour, but a description of events already under way in Israel. The unpopular PM is Ehud Olmert, who will today be replaced as leader of the ruling Kadima party in a ballot of its 74,000 members. Unless both fail to cross the 40% threshold, either foreign minister Tzipi Livni or former defence minister Shaul Mofaz will be invited to form a coalition and take over as PM.

Polls favour Livni, who, after the failures of S?gol?ne Royal and Hillary Clinton, might well be the best chance we'll get to see another woman reach the political pinnacle this side of President Palin. Don't count on it, though: Israeli primaries are notoriously difficult to call, determined more by grassroots organisation and unseen horsetrading than by national standing.

The world's diplomats are certainly rooting for Livni, believing that her involvement in the last year of negotiations makes her the best hope for peace between Israelis and Palestinians. She has impressed even her adversaries in those talks, leading a team described as serious and professional: one Palestinian calls Livni a "master negotiator".

If she now steps into the top job, that must bode well, bringing the long promised two-state solution within reach, right? Wrong. Conversations with those who have been involved on the diplomatic frontline for more than 15 years, those who have made the creation of a Palestinian state alongside Israel their life's work, suggest a new despair. With a heavy heart, they are concluding that the two-state solution is dead.

I sat down this week with Shlomo Ben-Ami, Israel's former foreign minister and lead negotiator at the failed peace talks at Camp David in 2000. He would prefer Livni to Mofaz, but he's past believing it will make any great difference. No longer does he think that the effort to reach an agreement with the Palestinians - a project which has endured, on and off, since the Oslo accords of 1993 - depends on having this or that person in charge. The serial failures are not "technical", but structural, built into the conflict.

On the Israeli side, the troubles begin with a system designed for paralysis. Under an absurdly pure form of proportional representation, coalitions are inevitable, with small, often extreme parties exerting veto power over larger ones.

What's more, the corruption inquiries that dogged Olmert also hobbled his predecessors. Under Israel's strict legal rules a PM can be indicted for actions taken long before he reached office. "We have Mediterranean politicians and a Germanic judicial system," smiles Ben-Ami. Any leader who inches towards compromise with the Palestinians knows Israel's hawks will be ready to call the police, armed with a file of dirt. Little wonder that not a single illegal outpost on the occupied West Bank, let alone a fully fledged settlement, has been dismantled in the past eight years. "Politics consistently defeats statesmanship in our system," says the former foreign minister.

Things are not much better on the Palestinian side. The nation is split, with Hamas ruling Gaza and Fatah dominant in the West Bank, and it is a truism that Mahmoud Abbas is weak. But it's not just a leadership problem, says one Palestinian negotiator, also a veteran of the campaign for a two-state solution. "You don't even have a Palestinian national movement," he says. The only movement is Islamic: Hamas. Fatah and the PLO are "hollow shells". Abbas lacks the national stature of Yasser Arafat; he cannot simply impose his will. Any deal he accepts has at least to come close to the demands of Hamas.

The result is that the two sides are like a pair of acrobats who can stretch every sinew to bend over backwards - but still not touch. As Ben-Ami puts it: "The Israeli maximum will always fall short of the Palestinian minimum."

But what of the polls that show clear majorities on both sides in favour of two states? These are so-called passive majorities, the sentiment of a public who wouldn't object if an accord came along but won't lift a finger to effect it. Meanwhile, on both sides stand impassioned minorities, whether Jewish settlers or jihadist militants, who will do whatever it takes to thwart the compromise any peace deal would require.

The result is deep gloom among the peacemakers. They search now for a "new paradigm". Could that be a single, binational state? "A nightmare," says Ben-Ami, a South Africa situation with no hope of a South Africa solution, given the presence of two national groups equal in number. More unilateral Israeli withdrawals are similarly doomed: after what followed the Israeli pullout from Gaza in 2005 - a Hamas takeover - there would be little support for a similar move in the West Bank.

Instead, there is renewed interest in an old, and once discredited, idea: the Jordanian option. Advocates say Israel would surely feel happier conceding the West Bank to a stable state such as Jordan, than it would to a volatile and split Palestinian movement. Of course, many Palestinians would regard it as a betrayal after decades struggling for independence. But, say the idea's backers, what is more important to Palestinians: a state, or an end to living under occupation?

Not so fast, I say - and not only because Jordan's ruling Hashemites might not be too keen to expand the Palestinian majority in their country. I understand the despair of negotiators who have worked in vain for a decade and a half, but I am not ready to give the last rites to the two-state solution just yet. For one thing - as the peacemakers themselves still believe - it remains the most just resolution possible. Both sides would get the self-determination they want, the statehood other nations take for granted. More important, it is, despite everything, still achievable.

Maybe not now, in today's environment. But no context remains static. If Israel's negotiations with Syria were to bear fruit, offering the prospect of a comprehensive settlement between Israel and its neighbours, the cost of the two-state solution might start to look more affordable to the Israeli public. If Hamas were to be ushered in from the cold, joining Fatah, the Palestinian calculus would change too. If there were serious economic incentives, perhaps funded by the Gulf states keen to score diplomatic points in their competition with Iran, that might change it again.

But none of this can wait. It has to be done now. Just because the conflict has gone quiet, with no daily bombs on the evening news, it does not mean it cannot explode into violence once more. And the impact of that rarely stays confined to the region.

What's needed, and with desperate urgency, is pressure from the outside. Not a last-minute effort, such as the one mounted by Bush last November, but a serious, engaged grip from - who else? - a new administration in Washington. That some of the most dedicated and ingenious peacemakers have now given up on the two-state option is surely warning enough. We have one last chance to make it work - before it truly is too late.