Does Nicolas Sarkozy really hate Benjamin Netanyahu? Does President Obama really sympathize?

And does it really matter?

The fleeting, private exchange between the French and U.S. presidents at a summit in Cannes, France, made international headlines, and its meaning is still being parsed by political pundits and pro-Israel activists.

The Anti-Defamation League was the only major centrist Jewish group to publicly rebuke Obama for the Nov. 3 exchange, which was overheard by several journalists at the G-20 summit who were plugged into a listening device monitoring the leaders that was switched on a few minutes early.

“I cannot bear Netanyahu, he’s a liar,” Sarkozy reportedly said -- no one recorded the exchange -- and Obama supposedly replied, “You’re fed up with him, but I have to deal with him every day.”

The ADL called the exchange “un-Presidential.”

“President Obama’s response to Mr. Sarkozy implies that he agrees with the French leader," the ADL’s national director, Abraham Foxman, said in his Nov. 8 statement. "In light of the revelations here, we hope that the Obama Administration will do everything it can to reassure Israel that the relationship remains on a sure footing and to reinvigorate the trust between President Obama and Prime Minister Netanyahu, which clearly is not what it should be.”

The ADL’s broadside surprised others among mainstream pro-Israel groups who thought the issue was best dealt with as the conversation was meant to be -- privately. One source reported hearing a top official at the American Israel Public Affairs Committee quipping, “Obama and Bibi talk every day? This is great news!”

Foxman told JTA that his organization’s policy is to respond to press inquiries, and in this case they were plentiful.

“We got a lot of calls asking for comment,” he said. “There is a certain threshold of calls, and this was one of those situations.”

Foxman said he recognized that leaders sometimes let down their guard.

“Listen, I would love to know what Obama thinks about Sarkozy,” he said, referring to U.S. frustration with the French leader’s tendency to go it alone diplomatically without consulting others.

Foxman added, however, that relationships are important.

“There’s no question, attitude informs policy,” he said. “It doesn’t overwhelm, but it does inform.”

Steve Rosen, a former AIPAC foreign policy director, said the exchange was revealing but its significance should not be overstated. Sarkozy is famous for his cutting remarks about other leaders, Rosen said.

“This is Sarkozy's habit and form of expression,” he said.

Foxman, for his part, said he was disappointed that Obama “didn’t dissuade Sarkozy, didn’t disabuse him.”

But pro-Israel Democrats close to Obama said that a stirring rebuke from one president to another might play well on TV’s “The West Wing,” but that it tends not to happen in real life.

“What you have is a one-sentence reaction to something Sarkozy says, which is a translation of a translation,” said one top Jewish donor, noting that French journalists transcribed a conversation in English into French, and then it was re-translated in American news reports. “Sometimes it has an exclamation point, sometimes not -- don’t put words into the president’s mouth!”

The donor also said that it was unfair to indict Obama absent a recording.

“We haven’t heard the tone of his voice,” the donor said.

Obama’s defenders also noted that in the same exchange, the U.S. president was taking his French counterpart to task for supporting full Palestinian membership at UNESCO, the U.N.’s cultural and scientific affiliate. Obama reportedly told Sarkozy that he “didn’t appreciate” Sarkozy’s failure to consult on the issue, but added “that is now behind us.”

“Whether Obama's sympathetic response to Sarkozy's complaint was genuine or merely a sympathetic nod to build rapport hardly matters,” Seth Chalmers, the assistant director at New York University’s Berman Jewish Policy Archive, wrote in a blog post. “In either case, our President's message was that, irrespective of the Israeli Prime Minister's personality, Israel's preferred course of negotiations rather than unilateral UN recognition of Palestinian statehood is correct.”

When queried in Hawaii by a reporter about the exchange, Obama sounded a similar note.

While the U.S. leader said he would not comment on “conversations that I have with individual leaders,” he then added, “The primary conversation I had with President Sarkozy in that meeting revolved around my significant disappointment that France had voted in favor of the Palestinians joining UNESCO.”

But Republicans said the exchange was further evidence that Obama was abandoning Israel.

“At a moment when the Jewish state is isolated and under threat, we cannot have an American president who is disdainful of our special relationship with Israel,” former Massachusetts Gov. Mitt Romney, a leading contender for the 2012 presidential nod, said in a statement.

Obama would not be the first American president with whom Netanyahu has clashed. During his first term in office, Netanyahu had a rocky relationship with President Bill Clinton. Even Netanyahu’s most prominent defender in Obama’s circle, longtime U.S. Middle East negotiator Dennis Ross -- who announced last week that he would be leaving the White House -- has noted the challenges of working with the Israeli leader.

In his 2004 book, “The Missing Peace,” Ross, who previously served in the Clinton administration, said that Netanyahu “would try to have it both ways,” seeking recognition for concessions that he promises but sometimes does not make good on.

Aside from its implications for American-Israeli relations, the Obama-Sarkozy exchange also highlighted the strained relations that some Europe leaders who are otherwise considered relatively sympathetic to Israel have with Netanyahu. Sarkozy himself once was considered friendly with Netanyahu, and German Chancellor Angela Merkel reportedly clashed earlier this year with the Israeli prime minister over settlement construction and the stalled peace process.

But Netanyahu’s defenders say it is unfair to blame the Israeli leader for the moribund state of the peace process. The Washington Post’s Op-Ed editor, Jackson Diehl, said the bigger problem has been the recalcitrance by the Palestinian Authority President Mahmoud Abbas.

“Netanyahu has been an occasionally difficult but ultimately cooperative partner,” Diehl wrote, noting Netanyahu’s embrace of a two-state solution and his partial settlement freeze.

He added that “Abbas, it’s fair to say, has gone from resisting U.S. and French diplomacy to actively seeking to undermine it. Yet it is Netanyahu whom Sarkozy finds ‘unbearable,’ and whom Obama groans at having to ‘deal with every day.’ If there is an explanation for this, it must be personal; in substance, it makes little sense.”