Abbas secured a major election victory to succeed Yasser Arafat as Palestinian president. But he hardly has time to celebrate his victory before his swearing in on 12 January.
Militant groups are already demanding that Abbas produce key concessions from Israel. And Israeli officials such as Foreign Minister Silvan Shalom are already asking Abbas to clamp down on militants.
"I believe that what is important now is that the new leader of the Palestinians, Mahmud Abbas, Abu Mazen, will take the strategic decision to dismantle the infrastructure of terror organizations on the one hand and, on the other hand, to put an end to incitement [to violence]," Shalom said.
The demands on the new Palestinian leader are huge. Nonetheless, experts interviewed by RFE/RL say the election showed Palestinian society and its new leader might be ready to take on some of those demands.
Ameer Makhoul heads the Union of Arab Community-based Organizations, an Israeli Palestinian group of nongovernmental organizations. He says the most important result from the election is that it showed the world -- in particular a skeptical West -- that the Palestinians are capable of democracy.
"The recognition, credibility that we are -- that with the stereotypes in the West that we are not democratic enough as a people -- that we are able to deal with our issues by ourselves, that we can control our life by ourselves as a people," Makhoul said.
Makhoul says that by voting for moderate Abbas, Palestinians showed they are ready to move in a new direction after four years of bloody uprising against Israel.
Ekiva Eldar agrees. Eldar is chief political correspondent for the left-leaning Israeli daily "Haartez." He spoke with RFE/RL by telephone from Jerusalem.
"Basically, I believe that the profile of the Mahmoud Abbas voter is a more established, mainstream Palestinian who is tired of the uprising and he wants something else. And he believes, probably, that Abu Mazen will be able to deliver the goods -- those goods that Arafat was not able, and failed, to deliver," Eldar said.
But how he gets there is the key question. Abbas has called repeatedly for an end to the intifadah, or uprising, and says he wants peace talks with Israel.
But as Shalom indicated, unless Abbas can get militants to join a cease-fire, his days may be numbered.
Militant groups have suggested they are ready to follow Abbas in truce provided he can quickly win concessions from Israel. But it's unclear how much time they will give Abbas.
Mahmud al-Zahar, Hamas leader for Gaza, spoke to Reuters today.
"We do not give anything for free and we do not take part in failed attempts. We say that the occupation must end and once it does, then we can discuss issues, and how to fulfill our objectives. We have the issues of settlers and the occupation in the Gaza Strip and we have settlements and an occupation in the West Bank and we have the issue of Jerusalem and the issues of the right of return and other issues which must be discussed. But we will not give these killers anything for free. This will not happen," al-Zahar said.
But it's also unclear to what extent Israel will accept a decision by Abbas to co-opt, rather than confront, militant groups. Abbas has repeatedly said he would not use force to clamp down on militants such as Hamas, which boycotted the elections.
Makhoul, for his part, believes the election process has shown Palestinians that their own internal unity is the only way forward.
"[Hamas] are not outside of the Palestinian people; they are an [integral] part of the Palestinian people, whether we like it or not. The internal unity of the Palestinians is an essential issue in the major conflict with Israel; the major conflict is with Israel, not within the Palestinian people. And in this, Hamas and the Fatah and the other fronts or extremes are in the same situation; they have different strategies, of course, which we have to unify as part of the state-building process," Makhoul said.
But those strategies differ radically. How Abbas or any other leader can reconcile a desire for peaceful compromise with the violent tactics of the militants is unclear.
In that regard, Makhoul believes that the strong showing of Mustafa Barghouthi, a pro-democracy activist who finished second with 20 percent, looks set to play a major role in future Palestinian politics.
Makhoul says young people desiring a change of generation in the leadership largely supported Barghouthi, a Soviet-educated physician who now leads the third major force behind Abbas's Fatah movement and Hamas.
"They want to unite the Palestinian people and don't want to see this zero-sum game, either Fatah or Hamas. They want to see coalitions [come to be] and that there is no [ignoring] of any group; and the Palestinian leadership should be taking that very seriously, I think, as a model for coalitions to be built," Makhoul said.
Barghouthi is a distant relieve of Marwan Barghouthi, a popular Fatah uprising leader who is now in an Israeli jail.
Analysts agree that Abbas will have to show progress fast and that he can deliver Israeli concessions on key issues. Palestinians are set to return to the polls in May to elect a new Legislative Council, or parliament. Hamas is expected to field candidates in that vote.
Abbas is expected to meet soon with Israeli Prime Minister Ariel Sharon. Israeli officials say there have already been repeated informal contacts between the two sides.
Israel is also seen as keen to make progress, as is the United States. Washington has supported Abbas strongly and the Bush administration looks set to make an investment in the peace process.
A new Israeli government, including the dovish Labor Party, was sworn in today. It will be tasked with pulling Jewish settlements out of Gaza and parts of the West Bank.