Barack Obama, they say, did not get on well with Bibi Netanyahu when he met him in Jerusalem before the American elections.
Mr Obama, who figured out the Middle East pretty quickly, apparently found Bibi arrogant and unconvincing in his professed desire for peace with the Palestinians. What Mr Netanyahu thought of Mr Obama is not known, but he could scarcely have tried to hide his election line: security for Israel, but no Palestinian state.
Much depends, of course, on whether Tzipi Livni will consent to join a Netanyahu government. For if Avigdor Lieberman slips into a ministerial position, Obama is in trouble. Does he congratulate a new Israeli prime minister who has introduced into his government a man who is prepared to demand loyalty signatures from his own country's Arab minority? How would that go down in the United States, where a similar proposal - for a loyalty pledge by American minorities, for example - would be a scandal?
But those Palestinians who believe that Lieberman should be in a Netanyahu administration - on the grounds that the "true" face of Israel would then be clear to all Americans - are being a little premature. Obama is not going to change the US relationship with Israel. American foreign policy - like that of most states - is based not on justice but on power.
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And with America enduring the worst economic crisis since the Depression, Mr Obama is not going to take on the Israelis. Those Arabs who still fondly hope that the new US administration will at last "stand up" to Israel are mistaken. And the Secretary of State, Hillary Clinton, who would like to be the next Democrat president, is certainly not going to anger Israel or its supporters in Washington.
If Mr Netanyahu does form a government, however, it will prove that the slaughter in Gaza did not help Ms Livni's efforts to form her own cabinet. Ehud Barak and Livni, the authors of the whole bloody offensive (with the active help of Hamas' own provocations), will simply put Gaza behind them - until Mr Netanyahu decides on a second round of the battle against "world terror".
Yet it's interesting to note how easily the connections between Gaza and the Israeli election have faded away. Indeed, when The Economist was surveying the Middle East earlier this month, it suggested that the outrage over the Gaza killings expressed by the Turkish Prime Minister, Recep Tayyip Erdogan, to Israel's President Shimon Peres at Davos was a "temper tantrum" which may have been "a ploy to please voters" before Turkish municipal elections next month. Yet the magazine merely noted that "the unconcluded Gaza war and the [Israeli] elections are intertwined in voters' minds..."
Mr Netanyahu, it should be remembered, said the Gaza war ended too soon. So are we waiting for Part Two? Or the next round in Israel's war with the Hizbollah? Israelis must sometimes curse the proportional electoral system that brings them the most ungovernable government coalitions. But the Americans will find it hard to dress up a new Netanyahu government as further "progress" in the Middle East "peace process".