Benjamin Netanyahu appears to have won the Israeli election, but at what cost to relations with the one ally Israel needs most, America?

If he retains power, as seems likely , there won't have been an Israeli prime minister more at odds with a US president in the history of the Jewish state.

Israel can no longer rely on the world's remaining superpower to have its back, as the Middle East slips further into chaos.

The price of Mr Netanyahu's election campaign is as follows.

The perception, following his speech to the US Congress two weeks ago, that he is only interested in an alliance with the conservative right of US politics.

Disgust in Washington at his comments that bordered on racist incitement on election day: "The right-wing government is in danger. Arab voters are coming out in droves to the polls. Left-wing organisations are bussing them out."

You can only imagine President Barack Obama's thoughts as he will have read these words in his morning Oval Office briefing.

His spokesman condemned the comments on Wednesday as "deeply concerning and divisive".

Josh Earnest said Mr Netanyahu had used "rhetoric that seeks to marginalise one segment of their population".

There is also anger in the White House and State Department at the impression they have been played for suckers by Mr Netanyahu on the question of a two-state solution.

US Secretary of State John Kerry, it seems, wasted nine months' shuttle diplomacy based on Mr Netanyahu expressing support for the idea.

But the mask slipped in the closing days of the election when the Israeli PM rejected the idea outright, warning against giving "territory away to radical Islamist attacks against Israel".

Should Israelis be worried? Don't their politicians have the right to say what they want in their country's own elections?

Israeli prime ministers have always cultivated close personal relationships with US presidents as a matter of necessity.

When Ariel Sharon needed US acquiescence as he pummelled the Palestinians in Jenin, he only got it because he was able to say to George W Bush: "Trust me, I need to do this."

In contrast there will be no such private understanding between their current successors, should Israel need the same kind of quiet support, or something more robust, say, over Iran.

The White House statement reacting to the Israeli election pointedly did not congratulate Mr Netanyahu, mentioning only the Israeli people instead.

Israel has always needed to present a calculated ambiguity on a number of issues.

That way other nations can give it the benefit of the doubt.

Mr Netanyahu's stark rejection of the two-state solution demolishes that principle.

Arab neighbours who might want to support Israel over Iran will find that much harder now.

Other more important allies will find it harder to resist calls to impose boycotts, diplomatic pressure or action against Israel in the United Nations.

Mr Netanyahu, the master tactician, has pulled off an impressive feat clinging to power.

But it may have left Israel isolated and exposed when it needed international support most.