The outcome of this week's Middle East summitry may hinge on the answer to this question: How hard does President Bush intend to push Israelis and Palestinians towards peace?
Drawing up a road map for such a settlement, as the US has done, is the easier part of the equation. Getting willing, continued participation from bitter adversaries will be far more difficult.
Mr. Bush has already made an abrupt turnabout by engaging in intensive Mideast diplomacy at all. When he took office, he and high officials in his administration insisted that such effort was fruitless, and a waste of energy and prestige.
Now he is following in the footsteps of Jimmy Carter and Bill Clinton. Virtually every US president since Nixon has come to believe that in this area of the world it is important to press forward in some sort of a process, no matter how "peaceless" the situation seems to be. "Without the involvement of the president of the United States nothing good happens" in the region, says M.J. Rosenberg, director of the Washington office of the Israel Policy Forum.
The overseas trip by Bush that began in Poland and Russia over the weekend and continued Sunday at the G-8 meetings in Évian, France, has already seemed to carry this theme: The US will continue to push its ideas for the future of the rest of the world, no matter what others think.
While Bush was not overtly dismissive of France, Germany, and other critics of the US action in Iraq in his early meetings and speeches, neither was he conciliatory. In Poland on Saturday, Bush noted that in recent months the US and its Atlantic allies "have seen unity and common purpose. We have also seen debate - some of it healthy, some of it divisive.
At the Group of Eight summit, Bush is scheduled to have a separate meeting with French leaders, among the most caustic critics of the US action in Iraq, that will provide a further reading on how convivial or muscular the US is at the moment.
Then it is on to the Mideast, which may offer the most telling assessment of the US approach to the world post-Iraq. Unless an eruption of violence or some other dire problem disrupts his plans, President Bush on Tuesday is set to meet in Egypt with Egyptian President Hosni Mubarak, and the leaders of Saudi Arabia, Jordan, and Bahrain, along with Palestinian Prime Minister Mahmoud Abbas.
On Wednesday he will move to Jordan and huddle with Mr. Abbas and Israeli Prime Minister Ariel Sharon, both separately and together.
Administration officials insist that they are now diving into a style of diplomacy they once eschewed because the situation, not their own policies, has changed. In the wake of the Iraq war, the White House now feels it can give a little impetus to what is going to be a long and difficult process.
The rise of Abbas has given the US a new Palestinian political leader with whom it believes it can make progress. Mr. Sharon's acceptance of the US road map - however conditional - has given all parties the chance for a fresh start in negotiations.
"What the president will do is talk to the assembled leaders about their responsibilities and about our responsibilities to try to push forward the peace," said National Security Adviser Condoleeza Rice at a briefing for reporters last week.
Whatever their outcome, the talks represent something of a change in the administration's previous position that the impetus for peace in the Mideast must come from the parties themselves.
No one can force Israel and its adversaries to a settlement. For peace to be lasting, it much be something in which the parties wholeheartedly believe.
But in a situation where the sides are so suspicious of each other - and so riven by their own internal politics - a push from a larger power might be necessary, according to some experts in the region.
The US seeks "to influence the outcome of conflicts everywhere. The notion that only the Palestinian-Israeli conflict is exempt from that seems to me irrational," says Henry Siegman, director of the US/Middle East Project at the Council on Foreign Relations.
Indeed, the moment Bush indicated he would be seriously involved in the matter, things began to happen, says Mr. Siegman.
Sharon accepted the roadmap, albeit while voicing reservations about security guarantees and aspects of any final settlement.
On the level of geopolitics, the stakes for Bush in this process are high. He conquered Iraq, in part, to reorder the entire Middle East. Yet without a lasting rapproachment between Israel and its neighbors the region will always be riven with conflict.
In the past US peace efforts have always foundered, in the end, on the mutual suspicions of the parties. But if Sharon really makes some effort to freeze construction of Israeli settlements in the occupied territories, and if Abbas can reign in Hamas attacks, suspicions may begin to abate.
"At least the beginnings will have been made," says Klaus Larres, the Henry Kissinger scholar in foreign policy and international relations at the Library of Congress. "That could gradually develop into a real process."
In the weeks and months to come, the White House is unlikely to be satisfied just with talking for talkings' sake, notes Mr. Larres. Whether you like their policies or not, it's clear that "the Bush administration has always been results-oriented," he says.
On the level of domestic politics Bush may be risking less. Conventional wisdom has long held that Jewish voters might punish a US president who was seen to be squeezing Israel for the sake of an accommodation with Palestinians.
But the vast majority of US Jews did not vote for Bush anyway. And many of them are eager for a jump-start to the peace process.
In this context, even if Bush does not succeed "he gets credit for trying," says Mr. Rosenberg of the Israel Policy Forum.
As always in the Middle East, the next cycle of violence will be the true test of diplomacy. When bombings and retaliation occur "it's very easy to fall back into the old patterns" of hostility, says Rosenberg.