Livni, long considered the obvious successor to Prime Minister Ehud Olmert, won the vote in her ruling Kadima Party by a hairsbreadth 431 votes -- only 1.1 percent of those cast -- from her surprisingly strong challenger, Transportation Minister, former Defense Minister and former Chief of Staff Shaul Mofaz.

Provided Livni can form a new government over the next 42 days, her narrow victory is likely to mean Israel will refrain from any pre-emptive action against Iran, at least until the Bush administration leaves office in January and probably well beyond that.

Livni has established a warm friendship with U.S. Secretary of State Condoleezza Rice. The new Kadima leader has even been ready to put her political prospects within Israel at risk to help Rice advance her Middle East peace initiative over the past 10 months, though the Annapolis process, in fact, has gone nowhere.

Livni has enjoyed a high regard with the Israeli public during her relatively fast rise. She has the reputation of being the Ms. Clean of Israeli politics. Arab interlocutors and diplomats in recent months from nations such as Egypt and Jordan have privately expressed their views to this correspondent that she is the only potential Israeli leader they believe would be serious about reviving and advancing the peace process with the Palestinians.

However, Livni's road to the premiership and winning a full term of office in Israel's next general election is so difficult that it makes swimming through a river filled with hungry crocodiles look easy.

To begin with, as Sima Kadmon pointed out Thursday on the ynet.com Web site of Israel's top-selling daily newspaper Yediot Aharonot, so far only 0.5 percent of Israelis have voted for Livni as a potential national leader. The number of votes that just won her the primary election in the Kadima primary to succeed Olmert, who is battling a major corruption and bribery probe, was smaller than the number of Israelis who came to hear Sir Paul McCartney perform, Kadmon wrote.

Livni may not even get the chance to form a caretaker or transitional administration: Her defense minister, Ehud Barak, who leads the Labor Party, and Binyamin Netanyahu, who leads the main opposition Likud Party, are already talking about forming a Labor-Likud-led coalition between them.

Labor and Likud are the two traditional-leading parties of Israel. Livni's Kadima was set up only four years ago. It owes its current leading position in the Knesset to the charismatic and across-the-board popularity and credibility of Gen. Ariel Sharon, who, as prime minister from 2001 to 2006, broke the back of the Second Palestinian Intifada.

However, Sharon was felled by a massive stroke at the beginning of 2006 and has been in a coma ever since. Olmert, during his two and three-quarter years running the state, also has run Kadima's credibility and popularity into the ground.

Polls make clear that if Olmert were to have led Kadima into the next election, it would have been annihilated and Netanyahu would have been swept into office by a wide margin.

Livni therefore faces the uphill challenge of making herself more attractive and credible to the Israeli public than either Netanyahu or Barak, both of whom are former prime ministers with unrivaled executive experience.

Both men proved unsuccessful and unpopular after their first terms of office and were swept from power by wide margins in elections. But both of them since have redeemed their reputations.

Netanyahu did so by reviving Israel's economy, against all odds, during his highly successful stint as finance minister. Barak has made his comeback by proving a forceful, effective defense minister. He approved a dramatically successful attack on a suspect nuclear installation being built by Syria with North Korean help. And he has rescued Israel's crucial ballistic missile defense program from the chaos his incompetent predecessor, Amir Peretz, left it in.

Labor has more seats in the Knesset than Likud, so Barak will angle for the prime minister's job, leaving Netanyahu presumably the choice between defense minister -- the only major office of government he has not yet held -- or a second stint as foreign minister.

If the times were peaceful, Livni probably could offer a more optimistic alternative to Barak, who is, in fact, a dove on talks with the Palestinians but a hawk on pre-emptively striking Iran, or to Netanyahu, who is a hawk on both issues.

However, with hamas in Gaza continuing to bombard Israel with low-tech Qassam rockets, Hezbollah in southern Lebanon more aggressive and confident than ever, and even Syria now enjoying the prospects of its biggest weapons boosts from Russia in a quarter-century, Livni will have the odds stacked against her in the next general election, whatever happens.

Livni's best opportunity would be to form a new government and prove herself a competent and decisive national leader. Even if Barak pulls his Labor Party out of the ruling coalition, Livni would have an outside chance of forming a government without Labor, but only if the Arab parties in the Knesset supported her. And that probably would be the kiss of death for her prospects in the next election. Distrust of Israeli Arabs as well as Palestinians is stronger than ever in an Israel still counting the cost of more 1,000 civilians -- many of them women and children -- slaughtered in the second Intifada, mainly by suicide bombers.

Condoleezza Rice is certainly rooting for her friend Livni to succeed: Livni's problem is getting enough Israelis to feel the same way.