The Israeli electorate moved to the right because Israelis feel that peace with the Arabs is not close, the Gaza war will grant them only a temporary reprieve, and the country needs to maintain its fighting spirit. Here is how I see the reasons for the move to the right.
(1) The war in Gaza did not end decisively. Israel did not finish the job of destroying Hamas for at least two reasons. The first reason is that it would have been difficult and costly in terms of Arab and Israeli lives to invade the densely-populated areas and retake Gaza. This was, in fact, what Hamas was hoping Israel would do; they were waiting and they wanted to make sure it would be bloody. Israel has had enough of Gaza and does not really want to resume control there.
The second, maybe major, reason was that the world wouldn't let Israel finish the job. The world complained about the innocent Gazans killed in collateral damage.
It would have been acceptable for Israel to allow Hamas to survive and continue its reign of terror inside Gaza if Hamas would just stop firing rockets at Israel. But Hamas has shown that it wants to continue its reign of terror outside Gaza as well. Hamas continues shooting rockets at Israel, even after the "cease fire." To Hamas, honor means retaining the right to kill Jews with impunity.
Now, Israel has to rely on the promises made by Western countries to help seal the Gaza-Egypt border against the importation of arms and ammunition, despite the historical unreliability of Western nations in coming to Israel's defense.
(2) The Israeli public is emotionally involved with the fate of Corporal Gilad Shalit, a young Israeli soldier who was abducted by Hamas a couple of years ago. The published photos of him show him as a baby-faced kid. His name appears on billboards and bumper stickers, and is painted on huge water towers, etc. The Israeli public is incensed that, against international law, Shalit has been held captive without Red Cross (or other similar organization) access to him. Hamas demands the release of prisoners with blood on their hands, major terror masterminds, in exchange for Shalit. The Israeli government is embarrassed by its inability to get him back.
(3) None of Israel's recent wars, including the Gaza operation, have ended decisively because the world complains loudly whenever Israel kills people and destroys buildings. Israel is accused of war crimes when she attempts to defend herself. Every other Western country that has had to fight similar wars has killed proportionally more civilians and destroyed more buildings, yet has not been accused of war crimes.
The world didn't utter a sound when Hamas, or Hezbollah in the previous war, bombarded Israel with thousands of rockets. Only when Israel defended herself did the world's complaints begin. Hamas leaders do not stand accused of war crimes, even though many of the accusations made against Israel would more logically apply to them.
This is interpreted by the Israeli electorate to mean that the outside world is prejudicially obstructive.
(4) Arabs everywhere, including West Bank Arabs (the presumptive "peace partners") and especially Israeli Arabs (citizens of Israel) demonstrated in the streets in support of Hamas. Israeli Arabs (citizens of Israel), to my knowledge, did not demonstrate at all in support of the Jewish citizens of Israel who were the victims of Hamas terror attacks, even though Hamas is widely known in the Arab world to be terrorizing the citizens of Gaza as well as the Israelis.
(5) Iran's development of a nuclear arsenal continues without serious opposition.
As for the willingness of the new government to work for peace, the leftists concentrated their support in Kadima (headed by Tzipi Livni), abandoning the dovish stance of both Labor and Meretz. The right split its support between Likud (headed by Bibi Netanyahu) and Israel Beiteinu (headed by Avigdor Liberman). Considering just the individual parties, Kadima won by a small margin (two seats), but considering the right and left as voting blocs, the two right wing parties won big. The power is on the right, and Bibi Netanyahu is the guy who will lead it.
Because there are many small parties and not just two major parties, it is impossible for one party to obtain more than 50% of the vote. The party with the most votes, therefore, has to form a coalition with other, smaller parties. It is possible that Tzipi Livni will not be prime minister because of her inability to form a stable coalition. If she is able to do so, her first move would be a continuation of the peace overture extended by Ehud Olmert.
If Bibi Netanyahu becomes prime minister he would probably be willing to consider a peace proposal, but would not make concessions based on sheer faith. However, the world is sure to put a lot of pressure on him to do just that.
The Arab reaction has been very disappointing. The Arabs complain loudly about how badly they have been treated by Israel - and indeed the occupation has been extremely harsh on the Palestinians - but when they had the opportunity to express sympathy with Israel over the rockets from Gaza, they chose instead to complain only about the innocent Gazans killed during Israel's defensive war. Consequently, the Arabs did not earn any sympathy in the eyes of the Israelis. They appear as intransigent as ever.
Israelis know that the Palestinian Arabs continue to teach their children anti-Semitic hatred and that that has not abated, as is evident from translations of the Arabic news and other television programs and newspaper articles. For example, see Palestinian Media watch http://www.pmw.org.il/, CAMERA http://www.camera.org/, MEMRI http://www.memri.org/ and Honest Reporting