For Benjamin Netanyahu, the formula for resolving U.S.-Israeli tensions came in the form of a flow chart.

The Israeli prime minister took the chart with him when he met with Obama administration officials and visited the White House last week, two weeks after Israel angered the U.S. administration by announcing plans for 1,600 new housing units in a Jewish neighborhood of eastern Jerusalem during a visit to Israel by Vice President Joe Biden.

But the flow chart presentation didn't quite do the trick, and Netanyahu's relationship with President Obama remains on the rocks.

At the outset of meetings with Obama, U.S. Secretary of State Hillary Clinton and the leadership of the U.S. House of Representatives, Netanyahu pulled three sheets of paper from a manila accordion folder. Two featured the Israeli bureaucracy that approves Israeli construction projects, and the third was a simple chart coded into about five colors: a sketch of a new, reformed Israeli system that Netanyahu envisioned replacing the existing one.

The point of Netanyahu's presentation was not that he was close to reform -- the third sheet was more of a wish than a plan -- but to illustrate how he wasn't directly at fault for spoiling Biden's visit. At any stage of the current process, an announcement by a mid-level Jerusalem bureaucrat could derail Israeli-Palestinian negotiations, Netanyahu explained.

There were several reasons the charts didn't work. For one they were in Hebrew, with print that was tiny and virtually unreadable. More substantively, however, Netanyahu's interlocutors were less interested in explanations about what went awry during Biden's visit and more in how Netanyahu could fix the problem -- namely, the plan to build in eastern Jerusalem.

The Palestinian Authority has made a freeze on Israeli construction in eastern Jerusalem a condition of restarting talks. The Obama administration, while frustrated with Palestinian stubbornness, was even less in the mood for Netanyahu's excuses.

Ultimately, Netanyahu did not offer what the Americans wanted: an unmitigated freeze on building in eastern Jerusalem. Israel considers the area, which Israel annexed in 1980 after its capture during the 1967 Six-Day War, part of its sovereign territory, but the rest of the world views it as part of the West Bank.

While some Israelis favor freezing construction in eastern Jerusalem and ceding much of it to the Palestinians in exchange for a peace deal, Netanyahu's coalition government includes at least two parties that would exit at the mere whiff of such a concession. If Netanyahu allowed for negotiations over Jerusalem, he could even lose a chunk of his own Likud Party.

During his visit to Washington, the prime minister nonetheless sought a formula that could extricate him from the humiliation of going home without a resolution. He met with Obama for 90 minutes on the evening of March 23 -- about half an hour longer than such meetings usually last -- and retired with his staff to the Roosevelt Room to come up with formulas that might please the president. Later in the evening they asked Obama to return, and the leaders talked for another 35 minutes.

But no resolution emerged.

The next day, Netanyahu and his advisers retreated to the Israeli Embassy for consultations, which was taken as a bad sign. Netanyahu continued to hope for a breakthrough, delaying his trip home and forcing his staff into overdrive. He finally gave up that evening, setting off for Andrews Air Force Base at 10:30 p.m.

All Netanyahu had to show for his trip -- originally scheduled to address the annual policy conference of the American Israel Public Affairs Committee, which gave him a warm reception -- was a pledge for yet another mission to the Middle East by George Mitchell, the Obama administration's special envoy to the region.

David Makovsky, a senior analyst at the Washington Institute for Near East Policy, said Netanyahu was undone by the lack of a long-term vision. Netanyahu's concessions to the peace process -- including a 10-month partial freeze on construction in West Bank settlements -- have had less to do with an overarching vision of peace with the Palestinians than with accommodating Israel's closest ally, the United States.

By contrast, Palestinian Authority Prime Minister Salam Fayyad has a deadline for statehood, 2012, and is building the institutions that would underpin his state.

"Abu Mazen can say where he's going," Makovsky said, using the nom de guerre for Mahmoud Abbas, the PA president. "Netanyahu can't, and that's not good."

The lack of progress has been clear in the language U.S. government representatives are using to describe the U.S.-Israel tensions over eastern Jerusalem.

"There are areas that they discussed last night, some of which they agree and some of which they disagree," White House spokesman Robert Gibbs said after Obama and Netanyahu met. "And as I've said, those talks are ongoing.”

On Sunday, after another few days of intense phone conversations between U.S. and Israeli officials, another spokesman, Tommy Vietor, told Politico's Laura Rozen that no understandings had been reached on eastern Jerusalem.

"This is an issue on which the U.S. government has had long-standing differences with multiple Israeli governments, and the president believes that the only way for the parties to resolve these issues is by returning to negotiations," Vietor said. "That's why we've been talking to the Israelis about how to create an atmosphere that will allow the negotiations to succeed. Those conversations have been productive and will continue, as will our conversations with the Palestinians, about how to make the talks successful."

In the absence of tractable success with the Obama administration, Netanyahu has invested hope in competing American political entities, including Congress and the Jewish community, as well as friends in the media.

The results have been mixed: Three-quarters of the U.S. House of Representatives, 327 members, have signed onto a letter urging the Obama administration to keep its differences with Israel private, and Netanyahu's meeting with the House leadership produced statements about wall-to-wall support for Israel on Capitol Hill.

"We in Congress stand by Israel, something we have a joint bipartisan commitment -- no separation between us on this subject," said Rep. Nancy Pelosi (D-Calif.), the House speaker. "In Congress, we speak with one voice on the subject of Israel."

Beneath the surface, however, it was not so sanguine.

Official statements of support following Netanyahu's meeting with the unofficial Jewish congressional caucus were lacking. Those in Capitol Hill meetings with Netanyahu were nonplussed by the presentation of the charts, some staffers said, and some left wondering if he understood the gravity of the rift with the Obama administration.

There was similar public-private dissonance within the Jewish community. In Netanyahu's March 22 speech to AIPAC, he received a rousing standing ovation for his declaration that "Jerusalem is not a settlement."

But Jewish organizational leaders, as energetically as they were defending Netanyahu and talking up the closeness of the U.S.-Israel alliance, privately expressed anxiety about the direction in which things were going. One said he jumped at each BlackBerry buzz.

The leaders, who did not want to speak for attribution, were not focused on the substance of the disagreement -- such issues were better left to diplomats, they said -- but on its mechanics. Both sides were stumbling: The Americans by denying Netanyahu the protocols due a visiting head of government, such as a photo op; the Israelis by relentlessly and anxiously leaking.

On Sunday, the Conference of Presidents of Major American Jewish Organizations issued a Passover statement reaffirming the closeness of the U.S.-Israel relationship, pressing the Palestinians to return to peace talks, noting the Iranian threat and pleading for an end to distorted accounts of U.S.-Israel tensions -- and, notably, to attacks on Obama, echoing Netanyahu's own call earlier in the day.

"I have recently heard anonymous, unworthy remarks in the media regarding the American administration and the American president," Netanyahu told his Cabinet at the Sunday morning meeting. "I would like to make it clear: I find these remarks to be unacceptable. They are from nobody acting on my behalf."