It looks as though with all of the votes counted except the IDF vote, the right wing bloc including Israel Beiteinu and SHAS has 65 seats in the Knesset vs. the left wing bloc led by Kadima with only 55 including 11 Arab party seats and 13 from Labor. Now Ehud Barak of Labor has stated that his party will stay out of any coalition and the two Arab parties that were voted out of the elections before the Supreme Court reversed the decision have stated that they will not serve with those who voted them out. If these two are true, the only way that Kadima can form a coalition would be with both Israel Beiteinu and Likud coming from the right wing bloc. Meanwhile Likud can form a coalition without Kadima as long as Israel Beiteinu and SHAS stay put.
Does Israel Beiteinu at least want to pretend to negotiate with Kadima? Of course, the less Bibi Netanyahu can take them for granted, the more they will be able to get from him in concessions. It is certainly true that Kadima will up the ante, but I have difficulty seeing Avigdor Lieberman sitting in on cabinet discussions about forming a Palestinian state in the West Bank.
Let's look at this from a perspective of political positioning. If you set aside the Arab parties for the moment, the Jewish voters in Israel are now tilted 65 vs. 44 to the RIGHT. The Secular LEFT is in shambles. Labor and Meretz were crushed in this election. Kadima itself has party members that tend toward the right and the party may well split if left out of the coalition. Several leading Kadima members are former members of Likud. That also means that the right-left split of the Jewish vote is actually worse than the numbers above would indicate. Some of the Kadima vote is actually center-right.
It seems to me that it would be politically expedient for any right leaning party to stay right and for any left leaning party to move to the right or to stand in stark opposition rather than to participate, hoping that opposition will help bring strength. The latter is the path already chosen by Ehud Barak for the Labor Party.
An alternative to the straight right wing coalition would be for a coalition of the "Nationalist Right" along with Kadima: This would be Likud, Israel Beiteinu, National Union, Jewish Home and Kadima, leaving out the Ultra-Orthodox parties, SHAS and Torah Judaism. This coalition would have 77 seats in the Knesset, an overwhelming majority, but basically, just as a right wing coalition would, it would have a mandate to abandon the peace process as it stands. The advantages of this coalition would be that the religious parties would have less influence and this coalition could have Livni as the Foreign Minister dealing with the United States, which in its own elections shifted significantly to the political left.
It is possible that there could be some sort of shared PM spot shifting between Livni and Netanyahu in this coalition, but the nature of the coalition would prohibit Livni from continuing the path established by Kadima to this point. Just subtract Kadima, which would leave the government with 49 seats, and add the religious parties' 16 seats to the coalition and you have a right wing bloc coalition. Netanyahu could expand the coalition out to 93 seats by adding SHAS and Torah Judaism, something that would prevent any party from collapsing the coalition by withdrawal, including Kadima. That does not give Kadima much strength.
If Ehud Barak is true to his word and Labor stays out, even if the Arab parties joined a coalition, Kadima would need both Israel Beiteinu and SHAS to form a coalition without the Likud. I have grave difficulty seeing Israel Beiteinu being willing to serve with the Arab parties or the reverse. There are also significant issues between Israel Beiteinu and SHAS, after all Shas spiritual leader Rabbi Ovadia Yosef said of voters who cast their ballots for Avigdor Lieberman's Yisrael Beiteinu party which opposes the influence of religious parties on secular Israelis, "Whoever votes for Lieberman gives strength to Satan." I do not think that such a coalition is feasible.
Kadimah realistically needs both Israel Beiteinu and Likud in order to form a coalition. Ultimately, the next government of Israel will lean much further to the right on foreign policy issues regardless of which parties the coalition contains.
Right now, it seems that the real debate is over three choices: having a RIGHT leaning coalition led by Likud and Israel Beiteinu that includes Kadima, one that includes the religious parties and not Kadima, or one that includes both Kadima and the religious parties.
Looking at that, if I had to say who won the election, it would be Likud and Israel Beiteinu.