As IDF ground troops engage deeper in southern Lebanon, racing against time to achieve as many military goals as possible before a cease-fire is announced, Israel's diplomatic effort is now directed at Washington, struggling to prove that there is no discrepancy between the way Israel and the US see the ending of the war. Deputy Prime Minister Shimon Peres - on what started off as a PR trip to the US and ended as a full diplomatic mission - found himself in the middle of the debate over how and when the fighting in Lebanon will stop. "It may take a week; it may take two weeks," Peres told the White House press corps as he left his meeting with National Security Adviser Stephen Hadley. But hours later, Secretary of State Condoleezza Rice went on national TV and stressed that the US is talking about "days, not weeks." The press was quick to pick up on these differences, and Israeli diplomats scrambled to assure all that everything is fine, and that the timetables of Jerusalem and Washington are still synchronized. Yet, as the war proceeds, the difference between "days" and "weeks" becomes more crucial for Israel. From an Israeli standpoint, it may mean the difference between achieving a significant military goal that will make the war look like a success, and a cease-fire with no grand finale. The cease-fire clock began ticking after the Kafr Kana bombing. Rice, who according to all accounts was furious at the incident and saw it as a turning point, returned to Washington determined to push for a cease-fire as soon as possible. At the same time, President Bush did not see the event as a reason for changing course, and stuck to his belief that a cease-fire should be declared only after a meaningful solution is found to the Hizbullah problem. Here, too, the press highlighted the differences, but a dinner meeting between Bush and Rice at the White House Monday evening ironed out the wrinkles and returned Rice to the familiar policy of preferring a "sustainable" cease-fire to an "immediate" one. Rice will be spending this weekend at Bush's Crawford Ranch in Texas - a sign that the differences of opinion have not had an adverse effect on the longstanding friendship between the president and his secretary of state. As time passed after the Kana bombing, the US administration began to believe that the event may not have had as much of a dramatic effect on the conflict as first thought. A senior administration official, holding a conference call with leaders of the American Jewish community Wednesday, said simply that the administration does not know yet if Kana indeed constituted a turning point in the war. "We know it had the potential of being one," the official said, but we're not sure that will really happen." As for Rice, she has now formally joined the club of US secretaries of state who believed they had the key to a solution in the Middle East, only to find their hopes and plans shattered in face of the actions on the ground. Former ambassador to Israel Martin Indyk was reminded this week of his mission with then secretary of state Warren Christopher to Damascus after the 1996 Kana attack. "We were humiliated by [Syrian] president Hafez al-Assad, who left Christopher waiting for a meeting," Indyk recalled. Others, too, went through the Middle East treatment: Each time James Baker came to Israel to talk about solving the Israeli-Palestinian conflict, he was greeted by new settlements; Madeline Albright was fed false promises by Yasser Arafat, and Colin Powell, when trying to broker a cease-fire during the second intifada, was dragged back and forth by Ariel Sharon who kept coming up with new conditions for any cease-fire. But like her predecessors, Rice does not seem to be disillusioned by the failure of her mission, and is not giving up. "Our effort is moving to New York now," the senior official said Wednesday, pointing at the upcoming discussions in the Security Council over the terms of the Lebanon cease-fire. THE AMERICAN goal now is to finalize a deal with the members of the Security Council by Monday, ensuring that the war is indeed over in "days, not weeks." This goal is also turning out to be more difficult than the administration had anticipated. The US partnership with France, which led to driving Syrian forces out of Lebanon over a year ago, collapsed this week after American and French diplomats failed to reach an understanding over the language of the UN cease-fire resolution, and on the preferred sequence of events leading to an end to the war. A foreign diplomat posted in Washington noted this week that one of the sources of strength of the Bush approach toward the Lebanon crisis is the lack of serious opposition from the Arab world. It is true, of course, that even the moderate Arab countries have voiced their reservations about Israel's military operation and its toll on the civilian population. But, according to the diplomat, no real pressure was applied. "The Arab leaders are trapped in a gap between their reading of the regional map and the passions of the people on the street, and they don't want this gap to be too deep," a senior administration official said, analyzing the Arab response. What this means on a practical level is that the US does not feel it is under pressure from the Arab world to stop the fighting immediately. The only source of pressure that may begin to penetrate the administration's decision-making process is coming from the home front - the conservative base of the Republican Party. The daily reading of news and op-eds in the American press became a difficult task for the president and his advisers this week, with some of his main backers on foreign policy issues making public their criticism against his conduct on the Lebanon issue. Richard Haass, who served under Bush as director of policy planning at the State Department, made fun of the president's claim that the war could turn out to be an opportunity for American foreign policy; Brent Scowcroft, who was Bush senior's national security adviser, put out a call for the administration to push for a comprehensive solution in the Middle East, instead of focusing on the immediate crisis; and Nebraska Senator Chuck Hagel, a mainstream Republican and possible candidate for the presidency, demanded that Bush force a cease-fire immediately, because "this madness must stop." Though the voices criticizing Bush's policy on the Lebanon war are growing, a recent poll suggests that the president's political instincts were right. A majority of Americans believe that the current involvement of the US in the conflict is sufficient, and more important, more than 40 percent of Americans don't want to see their government getting any deeper into the conflict. If Bush's plan plays out as he had intended, these Americans will have nothing to fear: The US will stay out of active involvement and will - at most - put a hint of pressure on Israel to make sure it wraps up the operation in a few days.