The unresolved dispute between the United States and Israel over Israel's refusal to halt building Jewish homes in the predominantly Palestinian West Bank has created a pivotal dilemma for President Barack Obama: How hard should he push one of America's most important allies in the Middle East?

So far, Obama has limited his pressure to calculated public comments, calling Israeli settlement construction illegitimate and a roadblock to a lasting peace agreement with the Palestinians that would include a Palestinian state.

Israeli Defense Minister Ehud Barak is scheduled to meet Obama aides Tuesday in the U.S. in the latest bid to find a compromise.

In the face of American demands that Israel halt all settlement building in line with the 2003 "road map" for Middle East peace, Israeli leaders are floating the idea of accepting a three- to six-month freeze on new construction in all settlements.

However, they'd continue to build thousands of West Bank homes that already are under construction. On Monday, Israel unveiled plans to build 50 new homes at a West Bank settlement to house settlers relocated from a West Bank outpost called Migron.

The State Department on Monday wouldn't rule out a compromise but reiterated the U.S. view of Israel's obligations. "A freeze on all activity relating to settlements, including natural growth, is what it says in the road map," spokesman Ian Kelly said.

Obama's dilemma is further complicated by Arab nations' insistence on a more-than-cosmetic settlement freeze before they make confidence-building gestures toward Israel that might help restart peace talks.

If a deal can't be worked out, analysts say, Obama has several ways to ratchet up pressure on Israel.

Short of freezing loan guarantees for Israel, the United States could try to enlist broader American Jewish support for halting settlement building or embrace European efforts to penalize Israeli exports made in West Bank settlements.

The United States for many years has imposed formal financial penalties on Israel for its settlement construction. The penalties have had little practical effect, but the process does give Obama a precedent for imposing economic sanctions.

"They can make the whole settlement project expensive in terms of embarrassment and money," said Roni Bart, a research fellow at Israel's Institute for National Security Studies.

Most discussions of American pressure focus on freezing U.S. loan guarantees, an issue that President George H.W. Bush first raised in 1991.

After the Persian Gulf War, hard-line Israeli Prime Minister Yitzhak Shamir asked Bush for $10 billion in loan guarantees to help the country absorb an expected wave of immigrants from the former Soviet Union.

The Bush administration balked, insisting that Israel freeze settlement building.

That friction, Bart said, contributed to Shamir's downfall. This should serve as a cautionary tale for Prime Minister Benjamin Netanyahu, who so far has rebuffed American pressure to freeze settlements.

"The sense that Obama is not a friendly president is not good for an Israeli prime minister," said Gershom Gorenberg, the author of "The Accidental Empire," a book on the birth of Israel's settlement movement. "It's not a secret how dependent Israel is on the U.S."

However, the struggle also cost the first President Bush substantial political capital and brought strident criticism from Israel's supporters on Capitol Hill. Some Republicans think that the issue helped cost him re-election in 1992.

The post-Gulf War dispute was resolved when left-leaning Labor Party leader Yitzhak Rabin became prime minister and the new government agreed to a compromise.

Rabin, whom an extremist Israeli settlement supporter assassinated three years later, agreed to an American plan to deduct the amount that Israel spent on settlements from the U.S. loan guarantees.

While these guarantees didn't involve granting Israel money, they allowed the country to borrow money at lower rates because the U.S. government was backing the loans.

When Israel faced another economic crisis in 2003 due to the bursting of the high-tech bubble and the second Palestinian uprising, it again turned to the U.S. for loan guarantees, this time for $9 billion. The request was granted under the same conditions.

Because Israel never used the full amount of these loan guarantees, however, it never faced any financial backlash as a result of the agreement, making the penalties meaningless.

"The United States was showing the world that it was punishing Israel for settlements, and Israel was getting 90 percent of the guarantees it needed and going on with settlements and everybody was happy," Bart said.

According to unofficial figures from the U.S. Embassy in Tel Aviv, the United States has deducted more than $1 billion from $6.6 billion in loan guarantees made available to Israel.

At present, the United States is weighing another $1 billion in deductions for settlement construction. Because Israel has used only $4.4 billion in existing loan guarantees, however, the financial penalties are likely to have no practical effect.

There are also steps the U.S. could take on the diplomatic front.

European countries already regard products produced in the West Bank as not being made in Israel and therefore not eligible for customs exemptions.

The European Union has been weighing tougher steps to ensure that Israeli companies aren't able to skirt the laws and receive preferential treatment for goods from Jewish settlements in the West Bank.

With American encouragement, the Europeans even could exclude settlers from visa exemptions. The U.S., which has a free trade agreement with Israel, could consider similar restrictions.

The U.S. also provides Israel with diplomatic cover in the United Nations, vetoing resolutions that it thinks are unfair or harmful to Israel, and the State Department said Monday that it would continue providing this cover.

Gorenberg said it was unlikely that the U.S. would cut military aid for Israel.

"The Americans have, since 1967, had this tension of whether or not to use arms supplies as pressure, because it's strong pressure and because they have seen it as positive that Israel can defend itself so the U.S. won't have to," he said.

In the past, American administrations that enter into policy conflicts with Israel would confront opposition from Congress, but so far there hasn't been much pushback to Obama's policies.

"Obama picked the best issue to pressure Israel. Of all the contentious issues, Israeli settlement is the issue where Israel enjoys the least support," Bart said.