WASHINGTON — Israel’s new foreign minister, Avigdor Lieberman, seemed perplexed during his visit to Washington last month: At a time when America and Israel agreed on all the big issues—from Iran and North Korea to Afghanistan and Pakistan— how could the little issue of Israeli settlements on the West Bank get in the way?

When he met with Secretary of State Hillary Clinton, Lieberman questioned the U. S. demand for a freeze on settlement construction, including the so-called “natural growth” of existing settlements. “We can’t suffocate ourselves: Babies are born, people get married. At minimum, we must provide for a normal way of life for these people,” Lieberman told Clinton, according to a senior Israeli official.

Israeli protests like this usually have had the desired effect. Administrations called publicly for a halt in settlement construction, but they acquiesced in private to the realities of Israeli politics. Prime Minister Binyamin Netanyahu must have assumed he could play the same game, blunting the White House by appealing to Israel’s supporters in Congress.

But this time, the settlements game has been different. The Obama administration has surprised the Israelis by its unyielding insistence on a freeze as a prelude to peace negotiations. And key members of Congress have backed the administration’s position.

That doesn’t mean any breakthroughs are imminent, however. The more the administration pressures Israel, the more concessions the Arabs seem to want.

The tough line on settlements starts with President Obama, who made clear his opposition from his first days in office. He is backed by Vice President Biden and Clinton, both former senators and longtime supporters of Israel.

An influential hawk on the issue is Rahm Emanuel, the White House chief of staff and a former member of the House Democratic leadership. Emanuel has special credibility as a strong defender of Israel’s security.

His father was born in Jerusalem and was a member of the militant underground organization known as the Irgun.

Emanuel’s view is that settlements are not a security issue for Israel but a domestic political problem. According to a senior White House official, Emanuel has argued that if the Israelis insist on expanding settlements, “You’re doing it on your own dime. We don’t want our credibility to be compromised as you work out your domestic politics. We’re not going to pay for that one.”

The White House believes that if it comes to a showdown, Netanyahu will compromise. His coalition government, the administration reasons, is too weak to sustain an open break with its key ally, the United States. His coalition will splinter. The administration already is talking with Ehud Barak, the Labor Party leader and defense minister, who might form a new government if Netanyahu falls.

It’s a hardheaded strategy, but it has one big flaw: The Obama team is assuming that if it can pressure Israel into a real settlements freeze, the Arabs will respond with meaningful moves toward normalization of relations — which will give Israel some tangible benefits for its concessions. But that hope appears to be misplaced.

“What will I do in exchange for a settlements freeze? Nothing,” says a senior Arab diplomat. “We’re not interested in confidence-building, or a step-by-step approach.” Instead, the Arabs would like Obama to spell out the details of a final agreement, now.

The settlements issue illustrates why the Arab-Israeli problem drives people crazy. Even if you achieve a breakthrough, there’s always another snag ahead. Welcome to the Middle East, Mr. President. You said in your Cairo speech that resolving this problem would require patience. You got that right, for sure.