Even as Israeli Foreign Minister Tzipi Livni's supporters are clinking champagne glasses, her political rivals have already begun circling. Livni won Wednesday night's Kadima Party primary by a mere 431 votes, inching ahead of her main rival, Transportation Minister Shaul Mofaz. That victory should put her in a good position to take over as Israel's next prime minister after the current PM, Ehud Olmert, resigns as expected next week. She would be the first woman to hold the job in nearly 35 years.

Still, nobody is going to make it easy for Livni. Under Israel's Byzantine system, when a prime minister resigns, it falls to the president (currently Shimon Peres) to ask a member of parliament to form a new government. Peres, who is also a member of the Kadima Party created by former Prime Minister Ariel Sharon in late 2005, will almost certainly choose Livni. The Kadima leader will then have a little over a month to caucus with Israel's myriad political blocs, trying to cobble together enough support to seat a government.

The problem for Livni is that many of the party leaders she'd need to form a new government are bitter political rivals who would rather push for early elections. And if she can't form a government, new elections are exactly what Israel will get, within three months. She knows for sure she can't count on the hawkish Likud chairman, Benjamin Netanyahu, who would love nothing more than early elections. Polls show Bibi trouncing Livni and other Israeli leaders if a vote were held today. (Asked this week whether he'd consider joining a Livni government, Netanyahu replied that he'd rather join Lehman Brothers.) The head of the dovish Labor Party, Ehud Barak, also said this week that he prefers early elections to a Livni-led government.

Barak may just be angling for political concessions. But if not, Livni's only other choice would be to court Israel's handful of tiny single-issue or religious parties. The Sephardic Orthodox Shas Party may join a Livni-led coalition for a price—probably in the form of a promise to fund child-welfare programs. She'd also likely need to reach out to the dovish Meretz Party and the Pensioners Party, a voting bloc of Israel's elderly that was a trendy protest vote in the last elections for PM in 2006. Still, a government made up of fringe parties—and led by a candidate with a 431-vote victory, doesn't exactly herald the kind of mandate required to lead Israel to a peace deal with the Palestinians. For Livni, it's way too early to celebrate.