WASHINGTON — President Barack Obama heads to Israel on Tuesday hoping, but little real expectation, that by smoothing rough relations he can help restart the Middle East peace effort that went nowhere in his first term.

Obama will not carry with him a detailed proposal for how Israelis and Palestinians might resume talks, such as the one he offered in 2010. He instead plans a listening tour in Jerusalem and in Ramallah to solicit views on what the two sides want and to explore what may be possible.

The White House has sought to lower expectations for Obama's trip, particularly avoiding any anticipation of a breakthrough on peace talks any time soon. Even a renewed diplomatic effort, should one begin, stands a good chance of collapsing again, they say.

Nonetheless, senior advisers say, Obama thinks time spent in public diplomacy is a worthwhile investment.

He is focused on "the broader role of public opinion in peacemaking," according to one administration official.

He is not alone in thinking that the kind of outreach embodied by a presidential visit can make a difference.

"Israelis would love to see that he cares, and that it's not just a cerebral effort, but something that comes from the heart," said former deputy Foreign Minister Danny Ayalon. "Israelis — as tough as we may be considered abroad — are a very, very emotional people. If you smile at them and show some kind of positive attitude, you see they melt."

That amounts to far more than just a popularity contest, Ayalon said. To achieve his foreign policy goals, he added, Obama will need to win over a deeply insecure Israeli public so that they, in turn, will pressure the government to take risks that could improve relations with the Palestinians. Under this theory, Israelis only go out on a limb for peace when they are feeling secure.

Former President Bill Clinton, who made four trips to Israel, said at the time that he believed reassuring the Israeli public was one of the most important roles an American president could play in Mideast peacemaking.

On that score, Obama has considerable work to do, with the Israeli public and leaders.

Obama and Israeli Prime Minister Benjamin Netanyahu have had a notoriously poor relationship — at times last year, the Israeli leader seemed to be rooting for Republican Mitt Romney to win the White House. With Obama and Netanyahu having both been re-elected, White House officials hope that, at minimum, the trip will ease that relationship and the domestic political pressures Obama has faced because of it.

Beyond Netanyahu, polls have shown many Israelis harboring suspicion of Obama that dates back at least to his June 2009 trip to Cairo in which he called for a "new beginning" in America's relations with the Muslim world.

A poll published Friday in the Maariv newspaper found that 38 percent of Israelis defined Obama's attitude toward their country as "hostile" compared with 33 percent who found it "favorable." More worrisome for Obama, only 10 percent of respondents said their opinion of the president was favorable, while the rest said their view was indifferent, unfavorable or even "hateful." Other surveys have found more positive views, but Obama clearly does not enjoy the sort of demonstratively warm relationship with the Israeli public that his two predecessors had.

Obama hopes to begin changing that perception, appealing directly to Israelis in a speech in Jerusalem and in the symbolism that permeates his schedule.

"The president has a very strong record of support for Israel and its security," said Ben Rhodes, deputy national security advisor to Obama, "but we also understand that there is no substitute for the president of the United States going to Israel and delivering that message directly to the Israeli people."

Obama will spend just a few hours in Ramallah, the seat of the Palestinian Authority, and the rest of his three-day trip in Jerusalem. He plans to visit Yad Vashem, Israel's official memorial to the victims of the Holocaust. He's scheduled to inspect an Iron Dome missile defense system, which was built with Pentagon aid. The system proved crucial in defending Israel during recent missile attacks and is constantly cited by officials from both governments as prime evidence of the U.S. commitment to Israeli security. He also plans to visit the grave of Theodor Herzl, the 19th century founder of modern Zionism, and view the ancient biblical manuscripts known as the Dead Sea Scrolls.

Those last two stops are, in part, an effort to fix the unintended effect of a line in Obama's Cairo speech. In telling his Egyptian audience that they needed to accept Israel's right to exist, Obama included a passage denouncing efforts to deny the Holocaust. But because he talked only about that subject, not other aspects of Jewish history, many Israelis took offense, saying he was ignoring their historic claim to the land of the Bible.

"This may not be readily apparent to an American audience, but for Israelis, and for the region, they are heavy with meaning," Michael Oren, Israeli ambassador to the U.S., said in an interview.

Even with intense attention to symbolic detail, however, any presidential trip can offend some party depending on whom and what the leader visits. Obama, for example, plans to speak to a youthful audience in Jerusalem rather than deliver a formal address to the Knesset, Israel's parliament. His schedule also includes the Church of the Nativity in Bethlehem, but not a mosque or the Jewish holy sites in Jerusalem's Old City.

The inevitable grumbling caused by such choices is among the reasons that presidents tend not to visit Israel often, with Clinton being the exception. Neither Ronald Reagan nor George H.W. Bush traveled to Israel during their presidencies. Presidents Richard Nixon, Jimmy Carter and George W. Bush each went near the end of their time in office.

As for the other side of the conflict, Palestinians say it can't hurt for Obama to try to smooth things over with Israelis. But after their expectations of the early Obama administration were unmet, they are reluctant to get their hopes up.

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Hanan Ashrawi, a longtime Palestinian legislator, said that while Secretary of State John F. Kerry clearly is interested in reviving the peace talks, "the jury is still out on whether Obama is going to give him the full backing he needs."

She said that if Obama "doesn't have a clear objective with a practical working plan and a binding timeline, it will be just treading water again" and that "he'd be better off not meddling at all."

Palestinian expectations, she said, "are extremely low."