“PRES OBAMA: SAVE ISRAEL FROM ITSELF.” So proclaimed a sign at a demonstration in late March in Sheik Jarrah, a neighborhood in East Jerusalem where activists gather every Friday to protest the eviction of Palestinian residents from their homes. Among the demonstrators was the Israeli novelist David Grossman, with whom I struck up a conversation about Barack Obama, who is not generally regarded as a popular figure in Israel these days, not least because of his public call for a halt to Israeli settlement activity. Some news sources have put his approval rating among Israelis as low as 4 percent.

Grossman, of course, first sounded the call about the folly of the settlements decades ago, in his searing book The Yellow Wind. (More recently, he is among the dozens of prominent Israelis that have signed an open letter to Elie Weisel deploring the evictions in Sheik Jarrah.) Not surprisingly, he voiced support for Obama, hedged only by concern that his administration might back off from its strong stand. “I just hope he continues in the same direction,” he said. When I asked why so few people seemed to share this view, he told me something a bit more surprising: Israeli public opinion is much more on Obama’s side than generally thought.

According to a March 19 poll in the left-leaning daily Haaretz to which Grossman referred me, this is true, with a startling 69 percent of Israelis viewing Obama’s policies toward Israel as “fair and friendly.” Conducted in the wake of the controversy surrounding Israel’s announcement during Vice President Joseph Biden’s visit that 1,600 new housing units will be built in East Jerusalem, the poll sought to determine whether the diplomatic skirmish had led Israelis to see Netanyahu “as a victim of overly strict treatment by the Obama administration.” To the contrary, “more people said Netanyahu’s behavior was irresponsible than said he acted responsibly,” the paper reported. Meanwhile, “a sweeping majority of Israelis think [Obama’s] treatment of this country is friendly and fair.”

But some critics greeted these findings with skepticism. As a breakdown of the poll in the Hebrew edition of Haaretz showed, 18 percent of respondents saw Obama as “friendly” toward Israel. Another 51 percent deemed him “inyani,” a Hebrew word for “matter-of-fact” or “businesslike” that Haaretz interpreted as “fair” (the word it used in its English edition). In an article titled “Haaretz Fiddled with Obama Poll,” the conservative daily Jerusalem Post suggested that this translation served to distort the poll results: those who called Obama “businesslike” might just as easily have been grouped with those who called him “hostile,” yielding a very different outcome. My own sense is that those who described Obama as “inyani” likely hold more ambivalent views than either newspaper suggested; they may represent the large number of Israelis who have lost hope in the peace process (and perhaps feel a certain nostalgia for the Bush era, when the White House’s backing was unqualified), but would still tend to support a US president who was serious about pushing for negotiations.

But if Haaretz overstated its case, it was not the first time the media has oversimplified how Israelis feel about Obama. Consider the assertion by FoxNews.com that “only four percent of Israelis… think President Obama is a friend of Israel”; or that Obama’s “approval rating in Israel is 4 percent,” as stated in a November 2009 editorial in The New York Times, which lamented that peace negotiations “may be father off than ever” because of Obama’s dismal standing among Israelis. In a speech before the Hudson Institute in Washington, D.C. last fall, Michael Oren, Israel’s Ambassador to the United States, described the lack of trust for Obama among Israelis as “one of the greatest obstacles” to peacemaking.

Yet the poll on which these conclusions are based is considerably more ambiguous than it appears. The 4 percent figure derives from a 2009 Smith Research poll taken on behalf of the Jerusalem Post. What the poll actually found was that 4 percent of Israelis viewed Obama’s policies as more pro-Israel than pro-Palestinian. Another 35 percent saw them as neutral; 10 percent expressed no opinion. So what do Israelis really think of Obama?

It’s true that a disturbingly large number of Israelis see him in crudely sinister terms: in the Haaretz poll, 27 percent of respondents said they believe Obama is “anti-Semitic.” I’ve heard more Israelis than I care to recall suggest that he has a special affinity for Muslims, citing his middle name or the fact that he spent part of his childhood in Indonesia. But antipathy toward the US President is not as widespread as some of the Netanyahu government’s spokesmen and supporters would like people to think. According to a survey of 1,000 Israelis conducted by Gerstein | Agne on behalf of the New America Foundation last year, a full 55 percent of Israelis regard Obama as honest and trustworthy, higher than the number who say this about Netanyahu. Moreover, a majority of Israelis described Obama’s election as good for addressing the world’s problems, and 41 percent held a favorable view of him, compared to 37 percent who held an unfavorable view. (Full disclosure: I am a fellow at New America, but was not in any way involved with this poll.)

These numbers are admittedly modest next to those of some of Obama’s predecessors like Bill Clinton, who Israelis adored even as he brokered a peace agreement many opposed. Yet Clinton entered office during the Oslo years, and Israel has changed in ways that would make it difficult for any American leader to speak frankly about issues like East Jerusalem and settlements without being dismissed in some quarters as an enemy. “The threshold of acceptance for criticism is getting higher and higher,” Akiva Eldar, a columnist at Haaretz and the coauthor of Lords of the Land, told me. “Now, in order to be titled ‘friend of Israel’ you need to agree with everything we are doing, or at least to shut up. Since Obama doesn’t shut up, he is not a ‘friend of Israel.’” It doesn’t help matters, Eldar added, that the last ‘friend of Israel’ in the White House set a standard Obama was bound to disappoint. “The message from Bush for eight years was that Israel can have it both ways: you can build settlements, fake a peace process and expect that business as usual will continue with the United States.”

On the other hand, while alienating the Israeli right, it is unclear whether Obama has made much progress in gaining the trust of Palestinians. Though much touted by the US, the “indirect” peace talks, which began last week, have been greeted by lack of enthusiasm and skepticism on both sides, in part because Obama’s break with the “business as usual” approach has struck some analysts as merely cosmetic. “We expect that the American administration would say to Israel: enough is enough,” complained Palestinian politician Mustafa Barghouti in a recent interview with Foreign Policy.

Even as he tries to restart the peace process, Obama has conspicuously avoided saying much of anything directly to Israelis: no speeches, no exclusive interviews with Israeli journalists, no visits. While such gestures would not endear him any further to the Israeli right, they could certainly influence the large number of Israelis who believe their country cannot afford to alienate the United States and know that it can’t possibly retain its Jewish and democratic character while continuing to annex more and more Palestinian land. This is true not only of the hundreds who’ve been turning out at demonstrations in Sheik Jarrah but also, one suspects, of a great many who told Haaretz that Obama’s approach toward their country has been “businesslike.”