JERUSALEM — What was the fight between President Bush and Israel Prime Minister Ariel Sharon all about?

That was a question that was on a lot of people's minds following a public disagreement between the two in front of reporters on Tuesday.

Some Jewish leaders said the disagreement was just a matter of semantics. Others said the United States and Israel were searching for a middle ground both could accept.

Either way, the bottom-line question is whether the cease-fire can survive.

Sharon angrily disagreed when Bush told reporters the parties should move to a cooling-off period following a "100 percent effort" on both sides to quell violence. Sharon shot back saying that an effort to quell violence wasn't sufficient, and that the period could only begin after there was a "full cessation of hostilities" for at least 10 days.

One of the main reasons for U.S. Secretary of State Colin Powell's current 4-day visit to the region is to press Palestinian leader Yasser Arafat to attempt to stop random attacks.

For Powell to get Arafat to exert more effort, he has to dangle a carrot. And that carrot is what Bush dangled Tuesday night: U.S. acceptance of the premise that if the Palestinians make a genuine, concerted effort to get the level of violence down to what it was prior to May 2000 — when al Nakba riots broke out — the process would move forward quickly and culminate in a return to negotiations.

The United States has been telling Israel for weeks, through Ambassador Martin Indyk, special envoy William Burns and via telephone conversations with Powell that the Palestinian Authority needs to see something immediate for their intervention thus far and cannot wait through a long cooling-off period.

The U.S. concern is that a six-week cooling-off period — which according to Israel's interpretation would begin anew after each act of violence — followed by three months of confidence-building measures would endlessly push off the time when the sides would actually have to sit down and negotiate.

The Bush administration is afraid of a long-term stalling tactic — one reason Sharon, accompanied by maps, drew the outlines of his long-term interim agreement for the president Tuesday, to show the U.S. president he has a plan.

Israel and the United States are in constant dialogue, so what Bush said at the press conference is not news for Sharon; he has been hearing it for weeks. But the public manner in which Bush chose to convey the message shows there is something else at play.

In addition to signaling to Sharon he would do well to internalize what various U.S. envoys have been telling him, Bush was showing his moderate Arab allies, who have been pressuring the United States to pressure Israel, that their arguments have not fallen on deaf ears.

Bush's public comments are an indication that when the Saudis talk, the Americans listen. And not only the Saudis.

In an interview with Associated Press last week, Powell made a point of saying that the Arab leaders he has met with have given the administration "good marks." Those marks, for a country both facing a serious energy crunch and interested in recreating the anti-Saddam Hussein alliance, are not something to be taken lightly.

Interestingly enough, the disagreement over 100-percent effort vs. 100-percent results is not limited to Israel and the United States. This point of contention also exists inside the government, specifically between Sharon and Foreign Minister Shimon Peres.

Until about two weeks ago, Peres — in numerous public appearances with visiting dignitaries and in statements to the press — had been demanding 100-percent effort. Granted, he said that Arafat should not be given "breaks" in implementing the cease-fire, but his overall tenor was that if Arafat is really trying, progress would not be held captive to any extremist able to hurl a rock or pack a can with nails and explosives.

The Prime Minister's Office, on the other hand, has long been speaking of a complete cessation of violence.

Sharon himself, in an interview with the Jerusalem Post in April, said, "The main thing is that we can only negotiate when there's total quiet. I stress that terrorism has to stop, and not that there's a decline in terrorist activities. If we agree to [returning to talks after a] decline in terrorism, we'll quickly find ourselves in an argument over how to define a decline in terrorism. If God forbid, one Jew is killed, whereas a week before, two were killed, is that a decline in terrorism?"

In other words, Sharon did not want to get into the details, because — as always — the devil is in the details.

Another huge "detail" looming just around the corner is the settlement freeze, an idea the government, which has accepted the Mitchell Report that calls for the freeze, has not precisely worked out with the Americans, or even with itself.

Case in point: the current spat between "officials close to Sharon" and Defense Minister Benjamin Ben-Eliezer over whether or not to uproot outposts in the West Bank that have sprouted up over the last few months.

But as the violence does decline, and as the Bush administration indicates its intent on forging ahead with the Mitchell Report timeline now, those types of details are going to loom very large, not only in Sharon's relations with the United States but in his relations with his senior coalition partner as well.