The Saudis have quietly been exchanging ideas with Israeli leaders on changes in the document that would make it more palatable to Israel. They also have been closely coordinating their moves with the United States and the Arab world.
For its part, Israel is working with the U.S. on a common front. The Israelis and Americans believe that the Saudi peace plan, with changes along the lines Israel is suggesting, could become a basis for comprehensive peace talks.
For the Saudis, regional stability is the name of the game. They identify two main sources of potential unrest in the region: the Israeli-Palestinian conflict and Iranian radicalism.
On the Palestinian front, the Saudis have made some striking moves. They've revived their 2002 peace plan and put it on the table for prior discussion with Israel; helped Hamas and Fatah reach a national unity agreement in Mecca; and provided the Palestinians with millions of dollars to help their struggling economy.
In other words, the Saudis have helped to create what some see as conditions for a new Israeli-Palestinian dialogue.
But more than trouble with the Palestinians, the Saudis are motivated by fear that Shi'ite Iran might act to destabilize their regime and that of other Western-oriented Sunni Muslim states by launching a terrorist war against them. They also fear that Iran's threatened attacks on American interests throughout the Middle East could destabilize the region.
The Saudis, therefore, are determined to persuade Iran to moderate its policies. That clearly jells with Israeli and American interests.
The Saudis do not oppose U.S. or, according to some reports, Israeli military action to preempt Iran's nuclear program and curb Iranian influence, but they prefer the diplomatic route. An early March meeting between Saudi King Abdullah and Iranian President Mahmoud Ahmadinejad was a last-ditch effort to halt the Iranians' drive toward nuclear weapons.
But it also was an attempt to get Iran on board for the peace initiative with Israel. After the talks, the Saudis announced that Iran was ready to accept the Saudi peace plan, which entails recognition of Israel.
If true, it would have been a strong added incentive for Israel to engage. But Iran denied it had accepted the plan, which indeed would have contradicted Iran's oft-stated aim to see Israel wiped off the map.
Nevertheless, no one disputes the rising Saudi influence.
"With the active encouragement of the White House, the Saudi king is becoming the No. 1 mediator in the Arab world, taking over the role from Egypt's President Mubarak," Arab affairs analyst Smadar Peri wrote in Yediot Achronot.
In her view, the Saudis have become key instruments of U.S. policy in the region. They've been using their economic and diplomatic muscle to prevent a sharp rise in the price of oil and to put economic pressure on Syria.
"The fear of the Iranian octopus is driving the Saudis and bringing about their growing closeness to the U.S.," Peri wrote.
It also is creating an identity of interests between the Saudis and Israel.
The key player on the Saudi side is national security adviser Prince Bandar Bin Sultan. Bandar, who served as Saudi ambassador to Washington for 22 years, has been mediating between the U. S. and Iran. Most important, he has been leading secret contacts with Israel over the Saudi peace initiative.
Still, American input on the Israeli-Palestinian and wider Israeli-Arab tracks will be crucial. With this in mind, some Arab players are trying to convince the U. S. to lean on Israel.
On the eve of a Washington visit, Jordan's King Abdullah II declared that the time had come for the United States to use its influence on Israel "to prove its transparency to the people of the region and that it is not biased."
To ensure the United States stays on its side, Israel sent two of Prime Minister Ehud Olmert's top aides, Yoram Turbovitch and Shalom Turjeman, to Washington to coordinate policy.
The main sticking point for Israel is the Saudi plan's prescription for millions of Palestinian refugees and their descendants. The 2002 formulation would give the refugees a right to return to Israel proper, which virtually all Israelis see as shorthand for the destruction of the Jewish state through a demographic onslaught.
In the secret talks with Prince Bandar, Israel has made it clear that the refugee option is totally unacceptable. Foreign Minister Tzipi Livni argues that in the context of a two-state solution, it's logical that Palestinian refugees would return to a Palestinian state, not Israel.
According to unconfirmed Israeli press reports, Saudi King Abdullah has ordered an appropriate change in the text. The plan, according to these reports, now says refugees will have a choice: either to return to the Palestinian state or stay where they are -- in Jordan, Lebanon or Syria -- and receive financial compensation.
The Saudis also reportedly hope to persuade Syria to drop its opposition to relinquishing the demand for a "right of return" to Israel in exchange for lifting Damascus' international isolation.
If the Arab League adopts this position in the summit in Riyadh at the end of March, it would constitute a dramatic change in the Arab position -- and, some feel, would force Israel to accept the revised plan as a basis for negotiation.
The plan offers normalization of relations with the entire Arab world, provided that Israel withdraws to its pre-1967 armistice lines and resolves its dispute with the Palestinians.
But the chairman of the Arab League, Amre Moussa, denies that there is Arab agreement on amending the Saudi plan. Moreover, even if the plan is changed, will the Palestinians agree to forego their demand for a right of return?
Hamas most certainly would not. It prefers to put off difficult final-status issues like refugees to a later date.
Therefore, in secret back-channel talks with an unofficial Israeli delegation, Hamas is proposing an alternative to the Saudi plan: a five-year cease-fire that would follow an Israeli withdrawal from most of the West Bank and the dismantling of all roadblocks. In return, the Palestinians would guarantee a cease-fire against Israelis "anywhere in the world."
None of this is a done deal. But after a long diplomatic drought, a number of interesting and thoughtful proposals are now on the table.
Leslie Susser is diplomatic correspondent for the Jerusalem Report