For President Obama, getting into a serious fight with Israel carries obvious domestic and foreign political risks. But it may offer the administration a payoff it sees as worthwhile: shoring up Mr. Obama’s credibility as a Middle East peacemaker by showing doubtful Israelis and Palestinians that he has the fortitude to push the two sides toward an agreement.

The risks at home were on display on Tuesday, as more than two dozen members of Congress, many of them Democrats, implored Mr. Obama to ease the tensions with the Israeli government after its announcement of a Jewish housing plan during a visit by Vice President Joseph R. Biden Jr.

The House Republican whip, Representative Eric Cantor of Virginia, called the White House chief of staff, Rahm Emanuel, to complain that the administration had seized on a minor diplomatic contretemps to try to impose its views on a loyal friend. Sarah Palin, the former Republican vice presidential candidate, issued a statement urging the president to “push the reset button on our relations with our ally Israel.”

For all the angst coming from Capitol Hill, however, the Obama administration seemed generally unruffled. And there were tentative signs that it was taking steps to cool the temperature.

Mr. Biden and Prime Minister Benjamin Netanyahu of Israel spoke by telephone on Tuesday evening, an administration official said. It was not clear what the two men talked about; aides to Mr. Biden did not return calls.

And earlier on Tuesday, Secretary of State Hillary Rodham Clinton reaffirmed the relationship between the United States and Israel, brushing aside talk of a crisis.

“Oh, I don’t buy that,” Mrs. Clinton said. “I’ve been around not that long, but a long time. We have an absolute commitment to Israel’s security. We have a close, unshakable bond between the United States and Israel and between the American and Israeli people.”

Mrs. Clinton did keep up the pressure on Mr. Netanyahu to demonstrate that he was committed to negotiations with the Palestinians

A senior administration official said the harsh rebuke of Mr. Netanyahu, delivered in a phone call last week by Mrs. Clinton, was important “to demonstrate we mean what we say when we enter these talks.” The announcement of a housing plan, the official said, undermined trust just as the United States was trying to open indirect talks between the Israelis and Palestinians.

“We felt we had to call that out,” he said, on the condition of anonymity because of the delicacy of the matter.

On the Israeli side, there were also efforts to calm the waters. Israel’s ambassador to Washington, Michael B. Oren, who had been widely quoted as saying that relations between Israel and the United States were facing a historic crisis, issued a statement saying he had been “flagrantly misquoted.”

“I am confident that we will overcome these differences shortly,” he said.

Taking a tough line with Israel helps the administration counter a perception that it folded last summer when Mr. Netanyahu rebuffed Mr. Obama’s demand that Israel freeze all construction of Jewish settlements. When Mr. Netanyahu countered with an offer of a 10-month partial freeze on the construction on the West Bank, Mrs. Clinton praised the offer as “unprecedented.”

That soured the Palestinians and left much of the Arab world wondering whether Mr. Obama would ever deliver on the promise in his speech in Cairo of a new approach to the Muslim world. American officials worried that this credibility gap could hinder their campaign to rally support from Persian Gulf countries for new sanctions against Iran over its nuclear program.

“For the nine months after the Cairo speech, people were saying, ‘Where’s the beef?’ ” said David J. Rothkopf, a former Clinton administration official who writes about foreign policy. “So far, engagement hasn’t worked anywhere. This might give them a chance to revitalize engagement.”

But Mr. Rothkopf, like others, sees as many risks as rewards. The harshness of the American response to Mr. Netanyahu, he said, could call into question the ability of the United States to manage its relationship with Israel. “The administration’s prestige in the region is damaged by its inability to manage the one relationship they are supposed to be able to manage,” he said.

Other analysts said the United States should not use a specific grievance over housing units to press a broad range of extremely difficult issues with Israel.

“I don’t think this issue should be like a Christmas tree, where you hang all these other ornaments on it,” said David Makovsky, a senior fellow at the Washington Institute for Near East Policy. “The whole episode should end where it began: you had a problem with those units, so you figure out how to fix it.”

But even some of Israel’s staunchest supporters in Congress said the dispute might focus minds on the larger prize. “It’s a moment for the Obama administration to say to our Israeli partners and our Palestinian partners, ‘We need to see peace,’ ” said Representative Gary L. Ackerman, Democrat of New York. “It’s a never-let-a-crisis-go-to-waste moment, and this is a mini-crisis, if even that.”

That message was echoed by Gen. David H. Petraeus, the commander of the military’s Central Command, who told the Senate Armed Services Committee that the lack of progress in the Middle East was a large challenge to American interests.

“The conflict foments anti-American sentiment due to a perception of U.S. favoritism toward Israel,” he said.