Tzipi Livni's appointment as Israel's justice minister is a significant first step in Binyamin "Bibi" Netanyahu's laborious construction of a new coalition government. Giving her the additional role of chief negotiator with the Palestinians appears designed to indicate a readiness to re-engage in the moribund peace process. But it is very far from a guarantee of success.

Livni's party - HaTnua (The Movement") — won just six seats in last month's election, which was characterized overall by a "lurch" to the centre rather than a widely-predicted shift to the right. Israeli Jews voted primarily on economic and social issues such as the cost of living and compulsory military service for the ultra-orthodox, who are currently exempt.

Livni, a founder of the centrist Kadima party, served as foreign minister under Ehud Olmert and led negotiations with the Palestinians in 2007-2008. As documented in the Palestine Papers, she was a combative negotiator with a wry sense of humour. Those talks, in any event, came to nothing. Israel blamed Mahmoud Abbas for not having responded to a "final offer." Palestinians say the deal was not nearly as generous as painted.

Under the terms of her agreement with "Bibi" Livni is to join his inner cabinet and be the exclusive negotiator with the Palestinians. Netanyahu has reportedly promised not to conduct separate talks to cut her out of the process.

It is an appointment that will likely be welcomed in Washington in advance of Barack Obama's much-heralded first official visit to Israel next month, unsubtly codenamed "Unbreakable Alliance". The US president gets on famously badly with Netanyahu, having blinked first in their confrontation over a settlement freeze in his first term. Livni's presence should at least help improve the atmosphere.

The extent of her influence will only become clear once the deal-making is completed and the new coalition is up and running. But in the ever-febrile atmosphere of Israeli politics her appointment was immediately criticized by Bibi's potential far right-wing partner, Bayt Yehudi, led by the annexationist Naftali Bennett. It is unclear what effect it will have on the centrist Yesh Atid, headed by the TV star-turned-politician Yair Lapid. Likud MPs also pitched in to attack Livni, as did Meretz on the left, accusing her of "betraying" voters.

Livni's defence was to insist that she was not prepared to serve as a "fig leaf" for policies she disagreed with — raising the question of whether her partnership with Bibi will survive very long. Netanyahu, she told Haaretz, understands the importance of the peace process. "He is aware of Israel's situation in the world. He is aware of the danger of international isolation. He understands the status quo cannot continue."

The make-up of Israel's next government — due to be finalized in the next two weeks — is of course only part of the story. Palestinians remain divided both politically and geographically between the PLO-ruled Palestinian Authority in the West Bank and Hamas, in control of the Gaza Strip. It is far from certain that Mahmoud Abbas has a popular mandate for any more negotiations with Israel. A third intifada might well win more support than a new bout of prolonged haggling over West Bank settlements, Jerusalem and refugees. Belief in the possibility of achieving a two-state solution is fading. Still, an Abbas adviser did welcome Livni's appointment as a "positive sign," praising her view that "settlements are an obstacle to peace."

On the Israeli side it seems unlikely that a government led by Netanyahu — with or without Livni — will be prepared to go far enough fast enough to produce meaningful and substantive negotiations with the Palestinians. Obama's position still probably matters more than who joins Bibi's cabinet.