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Abbas told a U.S. envoy in March that he believes a "historic" peace deal is possible.
At the time of Trump's inauguration in January, the Palestinians were much more jittery.
For weeks after the election, there had been no direct contact between Trump's aides and Palestinian officials. Politicians in Israel's right-wing government were declaring plans for an independent Palestinian state a thing of the past. And Palestinians were bracing for Trump to make good on his campaign pledge to move the U.S. Embassy to Jerusalem.
But an announcement on the embassy never came. Instead, Trump invited Abbas to the White House during a phone conversation in March. Several days later, presidential envoy Jason Greenblatt met with Abbas and groups from Palestinian civil society in Ramallah.
Although Palestinian officials note that the new U.S. president and his administration have barely uttered the words "two-state solution," Trump has spoken repeatedly about brokering the "ultimate" deal between Israelis and Palestinians.
"The fear has dissipated," said Elias Zananiri, a Palestine Liberation Organization official in charge of outreach to the Israeli public. "The Trump from before the election is a different Trump than from after the inauguration.''
Zananiri said the main item on Abbas' agenda at the White House is to learn from Trump how he intends to accomplish that "ultimate achievement."
"We want to hear about the substance, rather than emotion," he said. "Obama was emotional about the peace process, but it failed big time."
In the weeks leading up to the meeting, Abbas has made stops in Egypt and Jordan to get support from their respective leaders, President Abdel Fattah Sisi and King Abdullah II, for a Palestinian state.
There has been widespread talk here that the Trump administration wants to organize a summit to restart Israeli-Palestinian peace negotiations. In an interview last month with the Japanese newspaper Asahi Shimbun, Abbas said he would meet with Israeli Prime Minister Benjamin Netanyahu if Trump were to act as host.
Regardless of whether the meeting between Abbas and Trump produces an announcement on peace negotiations, the appearance of the two leaders together will be viewed as an achievement for the 82-year-old Abbas, who is struggling to remain relevant on the domestic and international stage.
Abbas, who hasn’t paid a visit to the White House in years, is grappling with flagging approval ratings, rising speculation about a potential successor from within his Fatah party, Israeli attacks on his credibility as a partner for peace and a 10-year standoff with
The meeting with Trump, experts say, will bolster Abbas' standing as the main Palestinian interlocutor on international politics.
"If you were Mahmoud Abbas, and you were facing imminent irrelevance, things have picked up now that you're meeting the president," said Khaled Elgindy, a former advisor to the Palestinian Authority leadership on peace negotiations who is now a fellow at the Brookings Institution in Washington.
"He gets to show that he's on the global scene and therefore relevant. It's a strong message to his domestic rivals and others in the region who are supporting his domestic rivals. It also is a message to Hamas, that 'I'm the address.'"
Ismail Haniyeh, a senior Hamas leader, predicted Sunday that Abbas' meeting with Trump wouldn't yield much for the Palestinians. The group grabbed the spotlight Monday by releasing a new manifesto that endorses the goal of establishing a Palestinian state in the West Bank and Gaza Strip but stops short of recognizing Israel.
Abbas has been turning the financial screws on Gaza's Islamist rulers in a bid to reassert the Palestinian Authority's influence over the territory.
The authority informed Israel recently that it will no longer foot the bill for the electricity that Israeli power plants supply to Gaza. It has also reduced the salaries that it continues to pay tens of thousands of former employees since Hamas took control of Gaza nearly 10 years ago.
Hamas is vulnerable to such pressure because Qatar is not renewing three months' worth of aid for electricity that it had been providing since January.
Abbas "is flexing what little muscle he still has," said Diana Buttu, a former official with the Palestinian negotiations support unit. "He needs to show that he is tough and in control."
Although Abbas and his aides are sounding upbeat about working with the new U.S. administration, only a fraction of Palestinians expect that Trump will be able to get peace negotiations restarted after a three-year hiatus.
A survey by the Ramallah-based Palestinian Center for Policy and Survey Research in March found that only 9% of respondents believed that Trump would help revive the talks, while 38% thought he was likely to worsen Israeli-Palestinian relations.
"I don't think Trump is going to pressure the Israelis," said Radi Jarai, a lecturer at Al Quds University in Jerusalem. "It was clear during Netanyahu's visit to the U.S. that President Trump did the things that Netanyahu wanted. And even when it came to the two-state solution, which was the basis of the peace process, Trump said 'I don't mind' if they choose one state or two states."
For all of the talk of "historic" and "ultimate" agreements, the geopolitical fundamentals that helped stymie the peace process under the Obama administration haven't changed. A large group in Israel's governing coalition remains opposed to a Palestinian state; Abbas is probably too weak domestically to be able to win support for painful compromises; and Arab states are preoccupied with more pressing regional crises.
"The optics of the Trump-Abbas meeting are good," said Elgindy, "but whether it will produce progress on a new diplomatic process is questionable."
Mitnick is a special correspondent.