MARGARET WARNER: These are tumultuous days in Palestinian politics. Over the weekend, members of the once-dominant Fatah Party took to the streets here in Gaza, and in the West Bank, to vent their frustration over the outcome of last week's election. They stormed the gates of Gaza's parliament, which the radical Islamic party Hamas will soon control.
The protesters demanded the resignation of Fatah's central committee, the old guard whose corruption, governing failures and campaign mismanagement led the party to defeat.
But while the losers were venting their anger, the winners were in round-the-clock meetings trying to come to terms with an election victory even they did not expect.
MARGARET WARNER: Newly elected legislator Saeed Siam, part of the collective leadership that runs Hamas, met with compatriots in Gaza to discuss the party's next steps. Though it won a huge majority in parliament -- more than enough to govern alone -- Hamas has urged the defeated Fatah faction to join in a coalition to run the legislature and the cabinet of the executive Palestinian Authority.
SAEED SIAM (Translated): The Hamas slogan is to empower the participation of all people. Fatah has been alone in power for years. We don't want to repeat that experience. We desire the participation of skilled people, both winners and non-winners. We want skilled people to serve the Palestinian people.
MARGARET WARNER: But Fatah for now is spurning the advances of Hamas, branded a terrorist organization by the West for its campaign of violence against Israeli civilians.
And the standoff over Fatah's future role is a hot topic of conversation in Palestinian coffee shops, workplaces and homes. Yesterday in Ramallah, 23-year-old Ahmed El A'm, head of a local wing of Fatah's armed Al Aqsa Martyrs Brigade, proudly pointed to a picture of himself in the newspaper brandishing an automatic weapon atop the parliament building in Ramallah.
AHMED EL A'M (Translated): We warn anyone on the Palestinian leadership against participating in this government. Today we will stand aside and let's see what Hamas can do for these people.
MARGARET WARNER: Many Fatah leaders are heeding that warning. Saeb Erekat, the Palestinians' chief negotiator with Israel, handily won re-election to parliament from his home town of Jericho. And he sounds eager to go into opposition to Hamas if it sticks with its vow to destroy Israel and create an Islamic state.
SAEB EREKAT: We will not be part of this government. We will be in opposition. And each week, we will demand from Hamas jobs, electricity, water, services, to expose corruption and the rule of law. We will have a demonstration each week to demand better services for our people.
MARGARET WARNER: But Palestinian Authority President Mahmoud Abbas, a member of Fatah, doesn't enjoy such clear-cut options. He is responsible for appointing a prime minister to form a cabinet acceptable to both the president and the new Hamas majority in the legislature.
Siam says Hamas wants President Abbas, who was elected last year for a four-year term, to continue in office.
SAEED SIAM (Translated): Our relationship with him is good; better than his relationship with Fatah. We want a real partnership with the president, and to agree on a program for the coming period.
ZIAD ABU-AMR: I think Hamas knows that Hamas alone can't do it.
MARGARET WARNER: Ziad Abu-Amr, reelected to parliament from Gaza as an independent with Hamas support, has been an intermediary between Fatah and Hamas in the past. He says Hamas leaders are pragmatic enough to know that they need help.
ZIAD ABU-AMR: Hamas is fully aware that it's not liked by the Americans and the Europeans. But if it's part of a national government under Mahmoud Abbas, who enjoys legitimacy, and who is known for his commitment to the peace process, this will make it easier for Hamas.
MARGARET WARNER: Hamas does seem ready to offer Abbas one carrot he's long sought, not the full disarmament of Hamas' military brigades, as he's demanded, but a finesse that incorporates them into the often hapless security forces that President Abbas' Palestinian Authority nominally controls.
But it's not yet clear that Hamas leaders, or their hardcore supporters, are ready to go further publicly recognize Israel and renounce violence as Abbas, Israel and the west are demanding.
MARGARET WARNER: Asked about compromises, Hamas leader Saeeb Siam in Gaza said the first step should come from elsewhere.
SAEED SIAM (Translated): I say go and ask Israel. Is it ready to recognize the rights of the Palestinian people and end the occupation? We gave negotiations a chance for years and the occupation did not end. Then Israel was pushed by force to leave the Gaza Strip. The problem lies in the occupation. If the occupation ends, we are ready for anything.
MARGARET WARNER: But on the other side of the barriers and checkpoints that separate the two societies, policy-makers in Jerusalem sound distinctly uninclined to make any gestures toward Hamas.
Tzahi Hanegbi is minister for strategic affairs, or internal security, in the Israeli cabinet.
TZAHI HANEGBI: Mahmoud Abbas cannot have relevancy if his government is going to be a Hamas government. This is the tragedy of the election results.
Mahmoud Abbas was elected in another campaign as a president. And he has his authorities. But if the legislative council would elect a Hamas government, it would be the end of our dialogue with the Palestinian Authority.
MARGARET WARNER: So what's the alternative?
TZAHI HANEGBI: We don't know. We are stuck. Everybody is stuck here.
MARGARET WARNER: Hamas leaders are floating one idea to get unstuck. They suggest that the Palestinian Authority they're about to join concentrate on domestic matters, and return negotiations with Israel to the Palestine Liberation Organization, or PLO, an umbrella group to which Hamas does not belong.
SAEED SIAM (Translated): The agreements with the Israelis were signed by the PLO, and there is no Palestinian law that gives a mandate to negotiate to the government. We want to put the train back on the right track.
MARGARET WARNER: But the man who for 12 years has actually done the negotiating emphatically says that idea is a non-starter.
SAEB EREKAT: When I go and give a report, I customarily give a monthly report to my colleagues in the council. So, what do I tell them? "I know that you don't recognize Israel and you don't accept negotiations as a tool to make peace, but I want to read you what I did with the Israelis last week?" You think that Israelis have a neon sign saying "stupid" on their forehead? Do you think that I have a neon sign saying "stupid" on my forehead?
And this is why we are urging Hamas to come down the ladder, to recognize the international relevant resolutions, the Arab League Peace Plan and the obligations of the Authority, and then the PLO can be in business.
MARGARET WARNER: This intense internal political jockeying under the watchful eyes of a nervous world is a first for Palestinians after 40 years of one party rule, and the outcome of that jockeying is not yet clear.
But there is one point on which the rival players in Gaza and here in the West Bank seem to agree: The Palestinians' dependence on foreign aid does give the West a big stick against Hamas, but it would be counterproductive for the West to use it yet.
The stick is large because of the intense economic crisis in the Palestinian territories, with debris-filled beaches and trash-filled empty lots, and legions of jobless men. The deficit-ridden Palestinian government desperately needs an injection of cash just to pay this month's salaries to 135,000 government workers and security forces.
But the Israelis for now are withholding $50 million in tax revenues collected from Palestinians, and the international community is also threatening cuts in aid.
Hamas insists it won't respond to being bullied, and threatens to go elsewhere for help.
SAEED SIAM (Translated): There is pressure, and I can even say blackmail, political blackmail from the international community, which is threatening to stop the aid. And this is unacceptable.
The international community should be morally committed to helping the Palestinian people. If they cut the aid, we have deep relations with countries in the Arab and Islamic world.
MARGARET WARNER: In the town of D'Ere Reballah on the outskirts of Gaza City even the ordinary man on the street understands that Hamas' victory could exacerbate the economic misery it was elected to address.
SAMY EL-AKLOUK, Coffee Shop Owner (Translated): Palestinian people are worried about Hamas' victory, worried about salaries, food. And workers are worried that all contacts with Israel will be stopped and they will have no jobs. They are worried that European aid will be cut too.
MARGARET WARNER: Even Hamas voters, like this vocational schoolteacher in town, recognize the Palestinians need the world in order to survive.
SCHOOLTEACHER (on screen): I think that the international community must play an important role to solve economic problems. As we know, we face an economic problem. We must find work. As you know, here is no work, the people here are jobless.
MARGARET WARNER: Political figures of all stripes here are urging the world to give Hamas some breathing room, out of self-interest, if nothing else.
ZIAD ABU-AMR: I think that the international community should not try to punish the Palestinian people for adopting the democratic processes.
MARGARET WARNER: So, are you saying that international pressure at this point is actually counterproductive?
ZIAD ABU-AMR: Exactly. Is it in the best interests of the Palestinian Authority, Israel, the United States, Europe and the quartet to see the existing situation deteriorating? Is it in the best security interest of Israel to have a state of chaos in the Palestinian territories?
MARGARET WARNER: Remarkably, even Israeli officials, as alarmed as they are by the election of a terrorist organization next door, are advising their global partners to go slow on aid cuts for now.
TZAHI HANEGBI: We're talking about people. They need medicines, they need food; they need their ordinary life. So I would say that in order to emphasize the resolve of the international community, it has to be at the beginning with diplomatic issues, and not right away with financial sanctions.
MARGARET WARNER: But even if the world does give Hamas a little breathing room, the group ultimately will have to make a choice. And it finds itself in a political box, owing loyalty to core supporters who back its radical stands.
But it also faces the reality that many of its voters last Wednesday were attracted by its anti-corruption message and record of community service, not by the violence for which Hamas is known worldwide.
SAEB EREKAT: For God's sake, 63 percent of the Palestinians -- I read a public opinion poll today -- 63 percent of the Palestinians want a negotiated, two-state solution with Israel. Analyze this.
MARGARET WARNER: In fact, Hamas has a lot to analyze, from inside and outside the Palestinian territories, as it ponders whether to compromise on its most basic principles as a price for being able to fully exercise the reins of power.