Much of the optimism is centered on Mahmud Abbas, the favorite in the coming vote. Abbas, a moderate favored by Washington, raised hopes in December when he called the four-year-old armed uprising against Israel a mistake that must end.
But in recent days, the campaign atmosphere has changed radically amid clashes in and around Gaza. Abbas has quickly shed his moderate speech for hard-line rhetoric.
Abbas yesterday called Israel "the Zionist enemy" after Israeli forces shot dead seven Palestinians in Gaza following a mortar attack on nearby Jewish settlers.
"We are praying for the souls of our martyrs who were killed today by the shells of the Zionist enemy in Beit Lahiya," Abbas said.
Israel immediately shot back. Foreign Minister Silvan Shalom said Abbas's remarks were unacceptable -- even in the heat of an election campaign.
"He [Mahmud Abbas] is using now terms that were not heard for a very long time," Shalom said. "And we believe that even during his election time, or during his election campaign, he can't use this kind of statements."
In another uncharacteristic scene, militants carried Abbas on their shoulders at a recent campaign rally in the West Bank. That incident drew criticism from U.S. Secretary of State Colin Powell.
Abbas has urged militants in Gaza to stop firing rockets on settlers, saying they only draw Israeli retaliation. His remarks drew protests from radical groups such as Hamas, who demanded he apologize and said they would continue to fire their "freedom rockets."
Abbas refused to apologize, but in a bid to appease the militants he said he would never take up arms against them.
Meanwhile, Abbas has said he favors the right of return of Palestinian refugees -- hardly a moderate position and a nonstarter for Israel.
Yet Abbas has also said he will not tolerate any internal challenges to the authority of the Palestinian Authority. And he said he wants peace negotiations, which first require an end to all violence.
Turi Munthe is an analyst at London's Royal United Services Institute. Asked about the new, apparently hard-line rhetoric, Munthe said Abbas is simply playing his cards to his domestic electorate.
"My view is that we have to see this as electioneering: Abbas's record over the years has been that of a moderate, we are just seeing him trying to gain as many votes as possible," Munthe said.
But if elected, Abbas will somehow have to transform his popular rhetoric into policies that unite all Palestinians.
For its part, Israel is adamant that the post-Arafat Palestinian leadership must rein in militants if there is to be progress toward peace. Israeli Prime Minister Ariel Sharon made that point again yesterday.
"We hope that a new leadership in the Palestinian Authority will choose to fight terrorism and push the reform process forward," Arafat said. "And, as I said in the past, we then would be willing to coordinate security issues and elements of the [Gaza] disengagement plan with that leadership."
Sharon said that getting out of Gaza will make Israel safer and may eventually lead back to the U.S.-backed road map, which proposes a two-state solution. But critics have said Sharon believes that leaving Gaza is the price Israel must pay to hold onto its large settlements in the West Bank.
Mouin Rabbani, an Amman-based analyst with the International Crisis Group, said Abbas -- or anyone else who might win this week's election -- can control the militants only to the extent that he can extract concessions from Israel.
"If he is able to go to the leadership of the factions, and to the commanders of the militants, with a clear plan that shows that as part of them ceasing their attacks, and laying down their arms, and so on, there is going to be an end to the [Israeli] occupation, the [militants] will be very hard-pressed to continue their attacks," Rabbani said.
On the other hand, if the new president goes to the militants empty-handed, merely expressing a preference for talks over violence, then he is likely to be scorned.
The irony of the Israeli-Palestinian conflict is that the same equation exists for the Israeli side. Lili Galili, a senior correspondent with the Israeli daily "Haaretz," said Israeli room to maneuver toward peace depends on concessions by the Palestinians.
"If the people who support withdrawal [from occupied land] see that the internal, domestic price within Israeli society is too high, and we get nothing, because Israeli citizens in the south are still bombed and shelled by Palestinian missiles, then it won't work, it just wont work," Galili said.
Galili said the unilateral withdrawal from Gaza might be a small step militarily, but it is a giant leap in terms of the mental change it requires from Israeli society.
Israeli radicals who oppose the withdrawal threaten Israel with civil war. So Galili said Israelis will question why the government is "tearing their society apart" if it secures no security benefits in exchange for that withdrawal.
"So there must be some balance between what happens here [in Gaza] and what we get in return," Galili said.
An end to the violence would be a start.
U.S. officials said yesterday that the Bush administration is considering ways to help bring that about. They reportedly include offering the new Palestinian leadership up to $200 million in aid in exchange for Palestinian efforts in stopping violence and carrying out reforms.