But there is no other viable candidate.
The Likud Party's Benjamin Netanyahu wouldn't consider such an offer because he prefers new elections. Polls show elections would deliver Netanyahu more than twice the number of seats Likud commands in the present Knesset.
Labor's Ehud Barak is not eligible because he is not a member of the Knesset.
Whether the country is headed for an early election should become clear fairly soon.
Livni says she does not intend to be dragged into a long coalition-building process. If in about 10 days she believes the chances of forming a government are not high, she says she will lead a move for new elections herself.
Despite all the obstacles and the recalcitrance of some of her prospective coalition partners, however, Livni is far more likely to succeed in forming a government than to fail.
Much will depend on the enigmatic Barak.
On the day Livni replaced Prime Minister Ehud Olmert as Kadima Party leader, Barak shocked the political establishment by meeting with Netanyahu and declaring that he would only join a national emergency government if it included the Likud leader.
It was a double-edged ploy by Barak: Put the onus of blame for not joining a national unity effort on Netanyahu, whom Barak knew would refuse, and create the impression in Livni's mind that he has an option of continuing to serve as defense minister in a Netanyahu government after elections and thereby upping the price for joining her coalition.
Barak's maneuvering stems from the dilemma he faces: If he joins a coalition, he helps the untried Livni establish herself as a credible national leader; if he stays out, he risks taking a hammering in early elections.
His biggest fear is that Livni will use him to form a government and in three months or so, on a wave of popular acclaim, precipitate a national election.
Barak's solution seems to be a readiness to join the coalition on two conditions: One, redefining the balance of power between him and Livni to create what he calls a "true partnership." Two, a guarantee from Livni that as far as she is concerned, the government will hold together for the full two years until the next scheduled election in 2010.
Barak hopes to create the perception of a two-headed Livni-Barak government from which he, too, will emerge two years down the road as a serious candidate for prime minister. Indeed, all of Barak's current coalition jockeying is about the 2010 elections.
Livni was quick to address Barak's concerns. In her speech accepting her nomination as prime minister-designate, she appealed to Netanyahu to join a national unity government, spoke of a "true partnership" with Labor and promised that her government would be for the long term.
Barak phoned Livni to congratulate her on her speech, and senior Labor politicians now estimate the chances of a Kadima-Labor agreement are high.
On paper, Livni has three broad coalition options:
1) A "national emergency" government including Labor and Likud. The argument for this is that Israel faces looming crises on several fronts and needs a unified Kadima-Labor-Likud leadership to meet them. The emergency government would be for a set time -- a year, for example -- with an agreed-upon date for new elections. Barak would stay on as defense minister and Netanyahu would be offered the Foreign Ministry or the Treasury. Livni would not need Shas, which is pressing for budget-sapping child allowances.Then again, if she is successful in forming a coalition with Labor and Shas, Livni may be able to reduce their leverage by bringing in additional coalition partners such as Meretz, Torah Judaism or even possibly the hawkish Yisrael Beiteinu.
But Netanyahu thus far has refused even to consider the idea. Despite Livni's public call and the fact that Netanyahu could be blamed for subverting national unity in a time of crisis, the Likud leader is unlikely to change his mind.
2) A "peace" government: This would be a minority government with the dovish Meretz Party instead of the Orthodox Shas Party. Ten Knesset members from the three mainly Arab parties would tacitly back the government from outside the coalition. The aim would be to cut a final peace agreement with the Palestinians and then go for a national election that would serve as a referendum of sorts on the deal.
But given Livni's hawkish background, her reluctance to be forced into make-or-break negotiations with the Palestinians and the certainty of vociferous right-wing condemnation, Livni is unlikely to go for a coalition dependent on Arab Knesset votes and Palestinian good faith.
But by keeping the door open to Meretz, Livni is pressuring Shas to moderate its terms for joining her government. She could even make a double gain by inviting the ultra-Orthodox Torah Judaism Party to join her peace government. This would give her a majority without Arab party support and without Shas. But Torah Judaism is unlikely to support peace policies that include concessions on Jerusalem.
3) A government based on the current coalition: Kadima, Labor, Shas and the Pensioners' Party. This is Livni's most realistic option. The problem here, however, is that Shas is caught between a possible deal on child allowances with Livni and Netanyahu's promises for more if Shas helps force an early election. Much will depend on how tough Livni is with Shas.
Until Livni forms a government, Olmert will remain the acting prime minister. How the actual business of government is conducted in the coming weeks will depend on the degree of cooperation between these two erstwhile political foes.
That's another reason for Livni to want to conclude coalition negotiations as quickly as possible. The smart money says she will have a government fairly soon -- its composition will say a lot about the direction in which she is likely to lead the country.