So, Barack Obama can lose his temper without a teleprompter. And we have the supremely aggravating Bibi Netanyahu to thank for that.

On St. Patrick’s Day, of all days, we wouldn’t want to think that our president did not know how to pick his donnybrooks.

The American government did unfortunately apologize to Col. Muammar el-Qaddafi, who got mad when a State Department spokesman correctly observed that the Libyan leader doesn’t always make sense. But in the case of a defiant Israel, the White House has not yet retreated into its usual compromising crouch.

Obama is so unpopular in Israel that he has nothing to lose by smacking our ally for its egregious treatment of the vice president. Joe Biden, the great champion of Israel, was humiliated when Israel used the occasion of his visit to defy America and announce a plan for 1,600 more homes in the disputed East Jerusalem area.

Israeli conservatives figured the American Eagle was toothless given that Obama had already backed down once on settlements. But the president has a lot to gain with Arabs disillusioned by the failure of the pre-emptive Nobel Prize winner to make good on his vaunted Cairo promise to resolve the Palestinian issue.

Besides, there is no love lost between the Israeli prime minister and Obama’s aides, Rahm Emanuel and David Axelrod — ever since Bibi obnoxiously labeled them “self-hating Jews” last summer.

The president and his inner circle are appalled at Israel’s self-absorption and its failure to notice that America is not only protecting Israel from Iran, fighting wars in Iraq and Afghanistan, but also dealing with a miasma of horrible problems at home. And Israel insults the Obama administration over a domestic zoning issue that has nothing to do with its security?

“That’s not how you treat your best friend,” said one Obama official.

During the campaign, Obama told The Atlantic’s Jeffrey Goldberg that “being a friend to Israel is partly to hold up a mirror and tell the truth,” to save them from themselves when they mindlessly let settlement gluttony scuttle any chance of peace.

After it was reported two weeks ago that Israel planned 600 other homes in East Jerusalem, Prince Saud al-Faisal, the Saudi foreign minister, warned me that Israel’s ultra-conservative religious groups were “killing every option that comes out that has peace in its objective.”

For the fundamentalist rabbis who run Israel’s working-class, ultra-Orthodox Sephardic Shas Party, the new houses represent earmarks. But it’s one thing to put earmarks in the budget and another to foment a crisis between Israel and its benefactor over them.

“It’s not entirely clear to me that the Shas Party knows who Joe Biden is or cares,” Jeffrey Goldberg told me.

“They have very narrow theological interests that don’t conform to the theological interests of American Jews,” he continued. “The high-tech entrepreneurs of Tel Aviv relate to the Shas Party about as well as the Jews of the Upper West Side relate to the Tea Party. The Shas Party is not overly attuned to the American-Israel relationship or the peace process.”

Goldberg also points out that “what most right-wing Israelis don’t understand is that even American Jews — especially the nearly 80 percent who voted for Obama — disaggregate what is in the best interest of Israel from what is in the best interest of the settlers.”

Obama knows that Jews no longer speak with one voice. That gives him enough room to keep the heat on Netanyahu. But the president’s smackdown also obscures the fact that the administration has no real strategy for peace and no impressive team below Hillary and Biden pushing for peace.

Arab leaders groused to me that Obama has gotten so weighed down by problems at home that he has lost the thread of his promises abroad.

In his Atlantic blog, Goldberg suggests that Obama’s ulterior motive is to drive out the ultra-conservatives and force a rupture in the governing coalition that will make it necessary for Netanyahu to take Tzipi Livni’s Kadima Party into his government, thus creating a “stable, centrist coalition” that could work for peace.

Netanyahu is taking his time-out in an Israel where many citizens and columnists are embarrassed by his behavior. Yet Post-Biden, the government is acting petulant and is inviting construction on more new homes in northeast Jerusalem. Perhaps Bibi will have the good sense to realize the Biden insult was a bit more than “regrettable,” as he tepidly put it. He may remember that the two most important things to Israel should be a security doctrine that prevents a neighboring adversary from getting a nuclear weapon and cherishing the relationship with America — rather than zoning and earmarks.

The Iranian mullahs must be laughing at the Americans and Israelis arguing about who insulted whom, while they are busy screwing their nuclear bombs together.