On Sunday, Israeli Prime Minister Ehud Olmert handed in his resignation. Israel’s Foreign Minister and the newly elected leader of the Kadima party, Tzipi Livni, has now been formally given the mandate by Israeli President Shimon Peres to build a governing coalition and thereby become prime minister. Olmert has faced ongoing corruption investigations, but the cloudy circumstances did not prevent him from leaving on a playful note. In convening the cabinet to inform them of his resignation, Olmert explained that there were a number of items on the agenda, and proceeded to give a rosy update on a series of Israeli weekend sporting successes--in the Para-Olympics, Davis Cup tennis, and the European basketball championship--before getting to the final item on the agenda, his own political demise.

Israel will now enter an intense round of political maneuvering. Livni has a maximum of forty-two days to convince a majority of the Knesset to support the coalition government she hopes to lead. In other words, Livni’s deadline falls tantalizingly on November 3--the eve of you know what. If she succeeds, her government could serve until the next scheduled election, which isn’t slated until November 2010. If Livni cannot form a governing majority, then elections will be called much sooner, most likely in February or March of 2009. And there is no guarantee that she’ll succeed.

Livni has already begun meeting with party leaders from the various blocs in Israel’s fractured Knesset in order to hit the magic number--61--she needs in order to pass a parliamentary vote of confidence. So it’s time to schmooze with the rabbis, the Pensioners, and most of all with mercurial Ehud Barak, the Labor leader. But Livni’s options are somewhat limited. The most predictable way forward would be for her to try to maintain the existing coalition of Kadima (29 seats), Labor (19), the Sephardi-ultra Orthodox Shas Party (12), and the Pensioners (seven, but now internally divided), and perhaps add the left-wing Meretz Party (five seats), which is already in conversation with Livni. As for the Likud and the rest of the right-wing and religious bloc, they favor early elections and a more profound change in government, Livni will not win them over. In effect, then, Livni’s task boils down to striking a deal with the Labor and Shas parties. The Shas playbook is by now familiar to most Israelis--they are all about the sectarian interests of their core constituency (seeking budgets for religious schools and institutions, special child allowances for large families, and the like). One rarely emerges unblemished from coalition deals with Shas. Moreover the Shas party leans to the right and is under electoral pressure from Likud, and diverges from her more moderate views on the peace process or negotiations about Jerusalem’s future.

Meanwhile, the Labor Party, and in particular its leader Ehud Barak, has become a somewhat unpredictable player. In recent days Barak has justifiably received some very bad press in Israel for postponing a meeting with Livni until after he could hobnobb with Likud leader Benjamin Netanyahu, and for, in consultations with his party, recommending to the president that he, and not Livni, be asked to form a government--despite the fact that this is a legal impossibility, since Barak is not a member of parliament. Barak--a former IDF chief of staff, a former prime minister and now the defense minister--is not a happy camper. Under Barak, Labor lags a distant third in the polls. He is bereft of an agenda, and having pushed hard for Olmert’s ouster, his initial refusal to cooperate with Livni comes across as transparently cheap politicking.

Worse yet, Barak’s approach to Livni seems to have a distinctly macho, sexist tone. As Israel’s leading columnist Nahum Barnea commented (referring to Barak) in the Yediot, “The boys aren’t willing to accept a girl into their game.” It’s hard to find a substantive reason why Labor would not serve in a Livni-led coalition: Barak has no discernibly distinct policies on socioeconomic issues, security issues, or peace-process issues, and many senior Labor Party officials are cringing at their leader’s behavior.

Livni naturally wants the government-formation process to go smoothly. But it seems clear that her potential allies will not allow that to happen. The question, and Livni’s dilemma, is this: How much tarnishing should she be willing to endure in the coming weeks to have a shot at becoming prime minister before elections are held? If it does come down to elections, Livni will have stiff competition from the Likud Party, led by former Prime Minister Benjamin Netanyahu. Current polling puts Netanyahu ahead in a tight race.

Haaretz political analyst Yossi Verter has described Livni’s appeal as that of a “non-political politician” who “stands for something else … radiates integrity, an upstanding character, and credibility … a Mrs. Clean.” She does not enjoy any comparisons to Israel’s one previous female Prime Minister, the unpopular Golda Meir. So, what should we expect if Tzipi Livni does form a coalition and becomes Prime Minister? She would have to assume that any coalition would not last the full two pre-election years and would thus need to chalk up some achievements in a relatively short period of time. The obvious arena, especially for someone with Livni’s Foreign Ministry experience, would be on the diplomatic/peace-process front. Livni would have to manage three diplomatic enterprises in which Israel is engaged--peace talks with the Fatah-led Palestinian Authority in the West Bank, the cease-fire and prisoner exchanges with Hamas in Gaza, and the Turkish-mediated talks with Syria. And hanging over everything else, of course, is always the potential for conflict with Iran.

Livni has established a reputation as a moderate. She favored a diplomatic solution during the Lebanon War of 2006 (and led efforts to achieve UNSCR 1701 that ended the war), she has led peace negotiations with the Palestinians, and she has avoided and sometimes criticized the more bellicose Israeli rhetoric about Iran. Clearly she has traveled some distance from her right-wing Likud and Jabotinskyist roots. But what is not clear is whether Livni can continue that journey and embrace a set of positions that would allow closure between Israel and its neighbors. Her red lines are not known on such key matters as one-to-one land swaps and minimalist deviations from the 1967 lines (including within Jerusalem), the prevention of settlement expansion, and actually implementing rather than just signing a permanent status deal.

Livni’s Manichean enthusiasm for thinking about the region in stark black-and-white terms of moderates versus extremists, is a cause for concern. The Middle East that Israel inhabits is full of grey areas, and dealing with Syria, Hamas, Iran, and a host of other issues will require pragmatic realism. Livni has not been a supporter of the ceasefire with Hamas--a ceasefire that, paradoxically, is one of Olmert’s more notable accomplishments. Hamas policy will be an early test for Livni, and to succeed she will almost certainly have to understand, as many of Israel’s military chiefs have, that there are no good military options. In private she is said to be more open on the issue than her public statements would make it seem. And on the Syria front, Livni has not been involved in the talks but has hinted that she would favor continuing them.

A Livni premiership could be effective and even positively game changing--if she can transcend Israel’s dysfunctional political system and constant coalition bargaining. But a lot will also depend on America. Livni has been close to Secretary Rice, and it is fair to assume that many of her more significant foreign policy choices will be strongly influenced by whether she is interacting with a President McCain or President Obama. So even if some of Israel’s questions are answered by November 3, others will have to wait until November 4.