The Kadima party, which is a fusion of factions from the Likud and from "Labor" lost most of its Likud supporters, who went back to the mother party but on the other side gained the support of "Labor" and Meretz voters. For some Meretz voters it was obviously like in the past voting for the "Labor" party ("bechol zot Ma'arach"). Livni gained so much because of the slogan Bibi or Tzipi. The pollsters defined the vote for Livni as a blocking vote, meaning that it meant to block Netanyahu. This was unlike the vote for the pensioners party Gil in the last elections, which was mainly a protest vote.
Barak's "Labor" actually gained because of the Gaza war, because before "Operation Cast Lead" the polls projected that it would win 6-7 seats and the elections it got 13 seats. One can say that Kadima and Labor gained because of the Gaza war and Netanyahu continuously lost support since the beginning of the war (see the enclosed graphic which depicts the Likud declines – the upper line - http://rotter.net/User_files/forum/499528c9466ae3be.jpg ).
Considering that there are no real differences on Palestinian issues between Likud, Kadima and "Labor" (if one does not take declarations of face value, but looks at the real policies), one can hardly talk about a shift to the right.
According to the analysts, Lieberman's gains are mainly coming according from the Gil Party that disappeared, Shas and other right-wing parties.
There is no doubt that Netanyahu wants a coalition with Kadima. He declared it many times. Just like he blocked the radical right-wingers in his own party (Moshe Feiglin and friends) he has no interest in building a government based on the support of the extreme right and they would not give it anyway, unless he makes some concrete commitments.
As it is, according to assessments of Israeli "experts", Netanyahu does not have the support of 61 seats that is necessary even to be invited to build the next government.
The main problem between Kadima and Likud is not ideological but that Livni wants to share the office of Prime Minister on a rotation basis as was the case in the '80s; and for the time being Netanyahu refuses.
In this poker game the winner will be the one with the stronger nerves. Lieberman's chance to be part of the new coalition are very low, not so much because of his racist position, but because of his demand to secularize the Israeli marriage system. In the last government he had this matter in the guidelines but it was not implemented. This time he promised to his voters that it will not remain abstract.
Along the line of this analysis the US president Obama is obviously asked by the Likud to pressure Kadima to form such a centrist government.
The enclosed Sunday Telegraph article seems to be inspired by the Likud, who is obviously very desperate to have Kadima on board but is not ready to pay the price Livni wants: a rotation in the PM job.
The article reads like a Netanyahu appeal to Obama to help him construct a centrist government
The bottom line is that the new Israeli government can be expected more or less to continue the line of the old one, i.e. of letting the so-called two-states option stay open while acting against it and slowly escalating measures against the Palestinians.
In the crude language of an Israeli sticker found also on Tela Aviv walls before the election:
"Whichever way we look at it, from Zipi and Bibi we are going to get Zibi!!!!"
*Arabic word for "my dick."