Ask Alan Greenspan to assess the prospects for Middle East peace and he’d warn everyone to beware of “irrational exuberance.”

Despite some promising rhetoric and a wave of optimism, the Bush administration appears to be taking seriously the advice of the Federal Reserve chairman who warned about excessive optimism among stock investors.

The president and secretary of state may sound enthusiastic about new prospects for peace, but they are moving very cautiously, dipping their toes into the water, undecided about plunging into negotiations, with all the obligations and risks that entails.

Secretary of State Condoleezza Rice stayed away from this week’s Israeli-Palestinian summit, explaining that such matters should be left to the locals. She has also shunned naming a full-time, top-level envoy to oversee the peace process and instead picked an army general to work with the Palestinians on security training.

This is a risk-averse administration that has largely avoided involvement in the Middle East over the past four years. But President Bush has been re-elected, there’s a new secretary of state with the president’s ear, Yasser Arafat is dead, and opportunity is knocking. Who will answer?

Rice said the parties themselves must want peace before anything can happen. That’s a given, but it can also be an excuse. More than half a century of experience has shown that even when the warring sides are ready for peace they can’t do it alone. And the only one who can help them is the United States. The Europeans, the United Nations and the Arabs, who have lost all credibility in Israel, are relegated to peripheral roles.

This week’s Israeli-Palestinian summit was strong evidence that both sides want to make certain the window of opportunity opened by Arafat’s death isn’t slammed shut. They need a fully engaged American government to keep that from happening.

Two years ago, American reluctance helped scuttle Mahmoud Abbas’ brief stint as Arafat’s first prime minister. President Bush left a summit in Aqaba with Abbas and Ariel Sharon declaring his intention to “ride herd” on the nascent hopes for peace. But his attention shifted, and the opportunity and commitment promptly disintegrated.

Middle Eastern leaders have to wonder whether this time will be different or déjà vu all over again.

With new opportunities opened by Arafat’s death and the successful Palestinian election, the big question is how deeply committed are the parties themselves, and will Bush get fully engaged this time. Or will they all miss another opportunity?

No one, including Bush, Sharon and Abbas, knows.

Bush has shown a deep reticence for what he sees as over-involvement. He will listen not only to Rice but to his political guru Karl Rove to assess the political risks at home. Full involvement will mean some disagreements with Sharon, particularly on issues like settlements and the security fence, and that won’t go down well with many of Bush’s big Jewish backers, who are often more hawkish than Sharon these days.

As he presses Sharon, Bush will be keeping an eye on those supporters to make sure they and their checkbooks remain in the Republican fold. The political pressure is already mounting.

Some Jewish groups on the right, already lobbying on Capitol Hill against Sharon’s Gaza disengagement, quickly announced a campaign against the $350 million in aid Bush promised Palestinians in his State of the Union address — an amount hiked by $40 million by Rice when she saw Abbas this week.

Bush also dropped his demand for establishing a democratic state as a prerequisite to American involvement, and Rice is now saying only that “they need to lay the foundation” for democracy.

Ironically, those in the Jewish community most supportive of a full-court press for peace by Bush are those on the left who voted overwhelmingly against him last November.

Some Jewish activists fear Bush may use pressure on Israel to help him mend fences with the European allies when he meets with them later this month.

Palestinians and Europeans want intense American involvement because they define that as pressure on Israel for concessions to the Palestinians. Sharon wants limited American involvement because he fears the Palestinian and European definition might be accurate.

Bush needs the Europeans to cover the major share of financial aid for the Palestinians. Peace will not come cheap. In 2000, when an agreement appeared possible during the closing months of the Clinton administration, the Israelis said they’d need several billion dollars for relocation and security costs, and the Palestinians wanted billions more for reconstruction and establishing a viable economy and government.

With the collapse of the Palestinian economy since the start of the second intifada, those costs have vastly escalated; on top of that, the Egyptians and Jordanians will demand to be rewarded for helping broker any deal.

European leaders told Rice that progress in Iraq is linked to progress in the Arab-Israeli conflict, and if Bush expects their help in the former they want a more substantive role in the latter.

Rice has reportedly confided to aides that she intends to get more deeply involved personally, and that she will insist Israel dismantle illegal outposts and freeze settlement construction — something Bush has been demanding for several years but Sharon has ignored with impunity. Rice is said to feel that such moves are vital to demonstrating American credibility as an honest broker.

Rice said this is “a time of optimism” and “fundamental changes” in the Middle East, and that Israel “needn’t worry” because “the United States will be there whenever needed.”

Even if Bush and Rice want to get more deeply involved in Israeli-Palestinian negotiations — which will collapse without them — they will also have to juggle explosive issues like Iraq, Iran, North Korea, Syria and the war on terror. That full plate will rein in any likelihood for irrational exuberance.

Douglas M. Bloomfield is a Washington, D.C.-based political consultant who was formerly chief legislative lobbyist for AIPAC.