A recent cartoon in the liberal Israeli newspaper Haaretz showed Prime Minister Benjamin Netanyahu breaking a sweat as he greeted a friend bearing gifts: President Trump with a package containing an Israeli-Palestinian peace process.
Mr. Netanyahu, on the heels of a famously bad relationship with former President Barack Obama that both sides did little to hide, has gone out of his way to signal that Mr. Trump is a president he can deal with. For his part, Trump took office after campaigning hard on the theme he would be a more sympathetic friend to Israel.
But what began with high expectations in the Israeli government of a suddenly freed hand in settlement building and of tightening Israel's hold on the occupied West Bank has turned into apprehension over what peace proposals the fast-pivoting Trump may bring with him on his visit here.
After a weekend meeting with Muslim heads of state in Saudi Arabia, the US president arrives here May 22, less than three weeks after hosting Palestinian President Mahmoud Abbas at the White House, and expressing optimism that he would succeed where others have failed.
Netanyahu's coalition, the most right-wing in Israel's history, opposes territorial concessions to the Palestinians to further the peace process and supports expanding settlements in the West Bank. And some key members oppose the notion of a Palestinian state altogether.
"For Netanyahu the really frightening possibility is that typically a peace process is accompanied by confidence-building measures, such as restraining settlement activity, the kinds of things that are difficult for him to do with his present coalition," says Nathan Thrall, an analyst with the International Crisis Group and author of "The Only Language They Understand," a new book on the Israeli-Palestinian conflict. "There is also a more general unease about Trump's unpredictability."
The president's unpredictability looms large in both Israeli and Palestinian calculations, analysts say. And the setting for the visit has changed rapidly in recent months.
In the weeks after Trump took office, Israel announced a building spree in the West Bank, publicizing plans for the construction of thousands of new homes in settlements, with no immediate response from Washington. After years of tension with the Obama administration over settlement construction, it seemed that the lid was off.
Trump's campaign promise to move the United States Embassy in Israel from Tel Aviv to Jerusalem, and his appointment of a new ambassador to Israel who is a staunch supporter of the settlements, seemed to point to a new policy direction.
Right-wing Israeli cabinet ministers celebrated a new era, floating proposals to annex large settlements to Israel, starting with the town of Maaleh Adumim near Jerusalem. Some hailed the demise of the two-state solution.
"Obama is history, now we have Trump," crowed Culture Minister Miri Regev, a member of Netanyahu's Likud party.
But then came signs that the Trump administration was not giving Israel a free pass when it came to the Palestinians. It started with a White House statement cautioning that building new settlements or expanding existing ones "may not be helpful," echoing the stance of previous administrations.
Then, in a meeting in Washington with Netanyahu, Trump publicly asked him to "hold back on settlements for a little bit." The Israeli government later announced it would take steps to curb the footprint of construction in settlements, limiting it to built-up areas of the settlements or zones contiguous to them.
After the presidential envoy, Jason Greenblatt, met Arab foreign ministers at an Arab League summit in March to discuss Israeli-Palestinian peace prospects, Trump met with Mr. Abbas and repeated his pledge to work for a peace deal. The White House later said Trump would endorse Palestinian "self-determination" during his visit to the region, diplomatic code for statehood.
Plans for moving the US Embassy in Israel to Jerusalem were put on hold after warnings from King Abdullah of Jordan and other Arab leaders that the move could spark unrest.
All of which has set the stage for a presidential visit to Israel and the Palestinian Authority whose substance is still very much an enigma. It remains unclear whether Trump will go beyond speeches to present concrete peacemaking proposals to the parties, or press them to take steps that could create a better atmosphere for renewed negotiations.
Still, his declared determination to push for what he has called the "ultimate deal" has the potential of unnerving both sides, who have gone out of their way to praise his leadership. Both could be asked to take politically risky steps.
Any concessions by Netanyahu would open him up to criticism from the right flank of his government, led by Naftali Bennett, head of the pro-settlement Jewish Home party, who has already accused the prime minister of failing to close the door on a two-state solution to the conflict.
"Abbas is worried that he will be pressured into entering a process that's damaging to him domestically if he's seen to be backing down on all the demands he has reiterated over the years," Mr. Thrall says. "If he's in a process with an Israeli governing coalition that finds it extraordinarily difficult to throw him a bone, how does he avoid looking like he is again giving cover to settlement expansion, land expropriation, and deprivation of Palestinian independence?"
Unpredictability is an issue
Trump's volatile personality and sharp policy swerves are another unsettling factor.
"Trump is a loose cannon, and even if he says something like 'Israel can depend on us' and sounds reassuring on concessions to the Palestinians, he may turn around the next day and say the opposite," says Yossi Alpher, an Israeli strategic analyst and author of "No End of Conflict: Rethinking Israel/Palestine."
"The only factor that might provide some sense of relief for Netanyahu is the impression that Trump doesn't have it in him to get committed to such a complex and extended process," Mr. Alpher says. "Given Trump's total unpredictability, Netanyahu is very cautious."
What has become increasingly clear is that the policies of the Trump administration are coming into line with those of its predecessors.
Like those that came before him, Trump's "current policy is opposition to building in the settlements, opposition to annexation of the West Bank and East Jerusalem, and support for Palestinian national aspirations," wrote Barak Ravid, diplomatic correspondent for Haaretz.
"It is doubtful whether Trump was familiar with the complexities of the Israeli-Palestinian conflict, but within four months in office he too has understood that there is really no other solution than two states for two peoples."