The latest effort to tip things the religious way comes from Eli Yishai, leader of the largest Orthodox party, Shas, who is minister of the interior.
ECONOMIST: Another row between the religious and the secular in Israel
But Labour's leader, Amram Mitzna, says he will not join, and the centrist Shinui party, which came third, will not share power with an ultra-Orthodox party.
Even more important is Mr Barak's agreement with the ultra-Orthodox party, United Torah Judaism, on new rules for the military conscription of students at yeshivas, or Talmudic colleges.
The ultra-Orthodox Shas party, a pivotal part of the government's coalition, has given notice that it will walk out if there is any negotiation over Jerusalem.
Ehud Barak's coalition government in Israel wobbled after the ultra-Orthodox Shas party said it would pull out after a row over money for its religious schools.
The ultra-Orthodox Shas party is likely to resist any change to Israel's draft law, and the pro-settlements Jewish Home party will likely resist attempts to restart talks with the current Palestinian leadership.
But the departure of the ultra-Orthodox Shas party, with its 17 seats, was a bitter blow, especially after Mr Barak had supported the party in its battle with another coalition ally, Meretz, over money for its religious schools.
The Centre Party had anyhow been coming apart at the seams, but Mr Barak is also having little joy from his two main coalition partners, the Sephardic- Orthodox Shas party and the leftist-secular Meretz party, which are at each other's throats over state finance for Shas schools.
The ruling Workers' Party has maintained orthodox domestic economic policies.
Another option open to Netanyahu is to offer either Yesh Atid or the Labor party to join him -- though that would risk a rift with his traditional ultra-orthodox supporters or even parts of his own party.
The Prosperous Justice Party, the most orthodox and popular group, has made tactical blunders and is unlikely to win more than 10% of the votes.
Netanyahu's Likud party has traditionally aligned with the ultra-Orthodox factions as coalition partners.
One consequence of the in-fighting has been the creation this week of a new centre-right party that will run on an explicitly anti-Orthodox platform.
As a religiously observant man and the son of the long-time leader of the National Religious Party, Mr Burg appeals to traditional and moderate-Orthodox voters.
The opposition will consist of Labour, the third-biggest party in the parliament with 15 seats, the ultra-Orthodox and Arab parties and centrist Kadima.
Yair Lapid, a longtime prominent journalist whose late father, Tommy Lapid, led Shinui, a onetime secularist party that took on the influence and power of the ultra-Orthodox.
Yesh Atid's leader is a dynamic figure -- Yair Lapid, a longtime prominent journalist whose late father, Tommy Lapid, led Shinui, a onetime secularist party that took on the influence and power of the ultra-Orthodox.
Small religious parties seek greater social spending for their constituents, while a party representing secular Russian Jews focuses on undermining a law exempting ultra-Orthodox Israelis from military service.
The 10-member Eritrean party included the heads of the four main religious institutions in Eritrea - the Orthodox Church, the Catholic Church, the Islamic Council and the Evangelical Church of Eritrea.
BBC: Leaders at prayer in Asmara (pic: Jorge Aramburu/UNMEE)
But the Yesh Atid party, a centrist movement devoted to helping the middle class and halting military draft exemptions for ultra-Orthodox civilians, came in a surprising second place with 19 seats, according to two exit polls, and 18, according to a third.
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