For weeks, President Obama has wrestled with his frayed relationship with key members of the American Jewish community. On Friday he will make his most public effort yet to repair the breach by doing something only three presidents have ever done: He will speak before an audience at a U.S. synagogue.

When Obama speaks in honor of Jewish American Heritage Month at Adas Israel, Washington’s most prominent Conservative synagogue, his task will not be to persuade the crowd to back his Mideast policies. Instead, he must forge an emotional connection with his Jewish listeners so they feel it in their “kishkes” — Yiddish for guts.

“That’s a real challenge for this president,” said Martin Indyk, who served as a special U.S. envoy for Israeli-Palestinian negotiations under Obama and belongs to Adas Israel. “It’s not simple to connect on the level of the kishkes.”

The conundrum Obama faces is one of a politician who shares a close cultural affinity with the liberal, social-activist Jews he has known for his entire academic and professional career but has never really connected with a national Jewish establishment that views him as insufficiently sympathetic to Israel.

And so he is going to Adas Israel, which has managed to hold the political center even as it has embraced a more progressive outlook in recent years. It is a synagogue that embodies the Washington Jewish elite, and Obama aims to demonstrate there that he feels their concerns in his bones.

In 2005, then-President George W. Bush tours the Historic Sixth and I synagogue with Rabbi Zvi Teitelbaum, left, and Shelton Zuckerman, vice president and treasurer of the synagogue. (Lawrence Jackson/AP)

As the District’s second-oldest congregation, Adas Israel has no match for its social and political credentials. Gen. Ulysses S. Grant outraged Jews by expelling them from the territories he oversaw in Kentucky, Mississippi and Tennessee during the Civil War. Grant’s December 1862 order was rescinded by President Abraham Lincoln the following month. But 13 years later, in 1876, Grant, then the incumbent president, sought to make amends by laying the cornerstone for the synagogue’s first building and donating $10 to the congregation.

Martin Luther King Jr. gave an address to a Jewish congregation at a citywide meeting held there in 1963, and every Israeli ambassador to the United States since the country’s founding has joined the congregation except for the current one, Ron Dermer. (Israeli Embassy spokesman Aaron Sagui said in an e-mail that Dermer attends a different synagogue because he does not drive on Shabbat and does not live within walking distance of the building.)

Many current and former Obama administration officials have attended services there, including Indyk, former deputy Treasury secretary Neal Wolin, former Federal Communications Commission chair Julius Genachowski and Robert Einhorn, the secretary of state’s former special adviser for nonproliferation and arms control. It is a place where at least two Supreme Court justices worship regularly during the High Holidays (Ruth Bader Ginsburg and Elena Kagan). Ambassadors make cameo appearances during bar and bat mitzvahs by providing Torah blessings.

“The president is probably the last person in the White House who hasn’t been to Adas,” quipped Norman Eisen, Obama’s former ambassador to the Czech Republic. “So I guess he wants to see what it’s all about.”

On Thursday, the Atlantic published an interview that its national correspondent Jeffrey Goldberg — one of many prominent D.C. journalists who belong to Adas Israel — conducted two days earlier with Obama about his Middle East policy and relationship with American Jews.

At a time when the politics of U.S. support for Israel have become increasingly polarized — with Israeli Prime Minister Benjamin Netanyahu delivering a joint address to Congress against Obama’s Iran policy in March, followed by Obama’s criticism of Netanyahu’s reelection campaign tactics a few weeks later — Adas Israel stands out as one of the few places where Democrats and Republicans still gather as a community.

“It’s a place where people can come and hang up their various affiliations and simply be a Jewish community and transcend political differences,” said its rabbi, Gil Steinlauf.

Steinlauf made news last year when he came out as gay to his congregation.

For supporters of Jewish American Heritage Month — a nine-year-old commemoration that has yet to “break out into broader society,” in the words of its foundation’s chair, Greg Rosenbaum — Obama’s speech offers a chance to introduce the holiday to a broader audience. Rep. Debbie Wasserman Schultz (D-Fla.) shepherded the resolution through the House in December 2005 as part of a package with a measure decrying what many Republicans called “the war on Christmas.”

“It is very important for a president to acknowledge, highlight and emphasize the contributions of our community,” Wasserman Schultz said, “so we can dispel harmful prejudices around the country.”

When George W. Bush signed the first presidential proclamation of the holiday in 2006, recalled former White House aide Tevi Troy, “It was pushing on an open door.” Bush himself toured the Historic Sixth and I synagogue in 2005 just before addressing a celebration of the 350th anniversary of the arrival of Jews to the United States at the National Building Museum, where he told the crowd, “This may sound a little odd for a Methodist from Texas saying this, but I just came from shul.” (Troy, who helped craft the zinger, coached Bush on his “shul” pronunciation.)

For Obama, Rosenbaum said, Friday’s event “is meant to indicate just how seriously he takes the Jewish community,” and “dispel some of that meme” that he is not fully supportive of Israel. Other top administration officials have made other overtures in recent weeks: Both Vice President Biden and White House Chief of Staff Denis McDonough attended the Israeli Independence Day celebration last month, and McDonough delivered an emotional tribute at this month’s retirement party for Abraham H. Foxman, the national director of the Anti-Defamation League.

There are a few obvious political imperatives for seeking to shore up ties between the administration and the reliably Democratic Jewish community. A Gallup poll last month found Obama had a 54 percent approval rating among Jewish Americans — 8 points above his overall standing with Americans, but a dip from the 13-point margin he has held on average since being elected. As the June 30 deadline for talks with Iran nears, support from the community could be pivotal in fending off attacks on Capitol Hill.

But on a more fundamental level, according to several of the president’s confidants, Obama is pained by the perception that he has not done enough for Israel. The president has had close Jewish friends for decades and inaugurated the tradition of holding an annual Passover Seder at the White House. “The president himself feels a little Jewish, in the sense that he identifies with Jewish values,” Indyk said.

For traditionalists like Foxman, however, Obama’s cultural affinity is one where he sees himself “as a liberal, progressive Jew. I want him to see himself, and act on Israel, as an American president, not as a conservative Jew or a liberal Jew.”

While the president has maintained a close security relationship with Israel, some of his comments have rankled some members of the community as being overly critical of Netanyahu’s government.

“He has not gotten the credit he deserves, in part because the public dissonance with Israel tends to drown out the good side of that equation,” said Dennis Ross, a distinguished fellow at the Washington Institute for Near East Policy who worked on Middle East issues under Obama, George W. Bush, Bill Clinton and Ronald Reagan.

That, in turn, has provided an opening for Republicans. New York Rep. Lee Zeldin, the only Jewish Republican in Congress, said this unease with Obama’s foreign policy has prompted some Jewish voters “to reconsider their lifelong loyalty to the Democratic Party, and they’re more open-minded toward change.”

But as Obama comes closer to leaving the national stage, his predicament may say more about how America’s vision of a two-state solution in the Mideast has been thwarted over the course of a quarter-century than a domestic political shift.

“Even the most determined presidents, with a clear understanding of what’s in the best interests of what’s involved, can’t force intransigent politicians to resolve a conflict they don’t want to resolve,” said J Street President Jeremy Ben-Ami, whose group backs a two-state solution. “And that’s where we’re at, unless they’re willing to put some more political weight behind it, which no one is willing to do.

Peyton Craighill contributed to this report.