If Tzipi Livni emerges as Israel's next prime minister it will be a sign that her party is willing to trust a politician without much military experience despite rising alarm over Iran. Of course, she would then have to glue together the current government or a new coalition. As Ehud Olmert, the incumbent, and too many predecessors have shown, being prime minister of Israel does not mean you can get anything done.

But if Livni overcomes those hurdles, she offers the best chance of edging forward talks with the Palestinians. These are caught in a half-life, sustained by a last burst of attention from President George W. Bush and Olmert, hoping for a deal by way of legacy, even if symbolic. But the talks have also been blocked by those two leaders' expired powers, as well as by the division of the Palestinian leadership between Hamas in Gaza and Fatah in the West Bank.

Yet if a new US president is to revive them, he will need an Israeli leader prepared to do so too. Livni is the best on offer. She has made an Obama-like case that change and "cleanliness" from the murk of the past should outweigh experience, although her critics are right to gibe that she has been carefully ambiguous about what she might do.

For the past four days, there has been a flurry of reports that Olmert is about to strike an outline deal with Mahmoud Abbas, Palestinian leader. Livni has been part of Olmert's four-person team which met again with Abbas and his negotiators yesterday night. The most solid ground, according to an Israeli official, has been the principle of land swaps: compensating Palestinians for West Bank territory now taken up by the main Israeli settlements with land elsewhere in Israel. Officials report that the talks have also covered the vocabulary which Israel might use to acknowledge the expulsion of Palestinians from its territory at its creation, without offering them the right to return. The status of Jerusalem, regarded by all sides as a deal-breaker at this low point of confidence, has been left out.

Times Archive, 1948: End of Palestine mandate

The Jewish National Council in Tel Aviv has proclaimed a new Jewish State of Israel. Mr Ben Gurion has been made Prime Minister

• Archive Topic: Establishment of the State of Israel

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These talks, since the Annapolis summit late last year, are the only tangible result of the Bush Administration's belated attempt to kickstart a peace process. US officials have argued that they have been worthwhile simply to keep contact alive until the next Administration. The noisy leaks are a sign of the intense desire of Olmert and Bush for something to brandish, more than a sign of progress on substantial issues. As one senior Palestinian official said, it is not as if they have discussed details of borders on a map, and his colleagues are wary that Israel will use reports of a supposed deal to make the Palestinians look churlish if none appears.

But if Livni wins, she will inherit a project that is still alive, even though it will need urgent effort. She has made clear that she stands in principle for the pursuit of a "two-state solution", although has been vague on crucial details. Shaul Mofaz, her chief rival for the head of Kadima, has leaned towards containing the threat of violence from Palestinians without perhaps offering a state. Benjamin Netanyahu, head of the right-wing Likud, who at the moment would gain if the government collapsed and elections were called, says that Israeli security would be unacceptably compromised by Palestinian sovereignty. (He has garnished that old pitch with a new riff about flying in evangelical pilgrims to kickstart a Palestinian tourism industry.)

Israeli public opinion about the talks is in a complicated state, both helpful to Livni's efforts, and undermining them. Many Israeli Jews appear to have accepted the principle of a two-state solution, and while exhausted by the subject, have a basic support for their leaders' efforts to pursue that goal. That has drained much heat out of the issue, as has the success of the separation barrier and the West Bank clampdown by Israeli forces in reducing suicide attacks. Israeli commentators acknowledge, too, that Fatah has improved its own security control in the West Bank.

But on the other hand, the apparent "containability" of the threat of Palestinian violence behind the barrier has allowed some to think that this is a solution not needing immediate improvement, and that the presence of Israeli forces in the West Bank is an adequate answer to Palestinian radicalisation. Many now say that Iran poses a far more urgent threat to the existence of Israel, and inevitably, the image of Iran potentially armed with nuclear weapons is so vivid that it sucks energy away from older, intricate deadlocks.

Livni has avoided saying whether she would support an Israeli military strike on Iran, while trying to dispatch complaints that a leader without deep roots in the military would not protect Israel in a crisis. But if she can satisfy those complaints, she is best placed to make progress on Israel's older, closer problem.

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