Back home, things are heating up. There is anger in the West Bank, both on the streets and within the ranks of Mr Abbas’s Fatah movement. The trigger is a two-week-old hunger strike by Palestinian prisoners.
Last Thursday, Palestinians shuttered their businesses in a show of solidarity, and the next day youths clashed with the Israeli army in a “day of rage”.
About a quarter of the 6,500 political prisoners held by Israel – almost all of them in Israeli territory, in violation of international law – are refusing food in protest at their degrading treatment. They want reforms to Israel’s industrial system of incarceration. Some 800,000 Palestinians – 40 per cent of males – have passed through Israel’s cells since 1967.
Israel hopes to break the prisoners’ spirits. It has locked up the leaders in solitary confinement, denied striking inmates access to a lawyer, taken away radios, and last week began confiscating salt rations – the only sustenance along with water the prisoners are taking.
The strike is led by Marwan Barghouti, the most senior Palestinian leader in jail – and the most popular, according to polls.
Mr Abbas is publicly supportive of the strikers, but in private he is said to want the protest over as quickly as possible. Reports at the weekend revealed that he had urged Egypt’s president, Abdel Fattah El Sisi, to intercede with America and Israel to help.
In part, Mr Abbas fears the influence of Mr Barghouti, a man often described as the Palestinian Nelson Mandela and seen as Mr Abbas’s likely successor. Notably, the Palestinian president has repeatedly sidelined him within Fatah.
But Mr Abbas is also concerned that the hunger strike will provoke violent clashes in the West Bank with Israeli security forces, damaging his efforts to persuade Mr Trump to back his diplomatic campaign for Palestinian statehood.
Instead, he wants to prove he can snuff out any signs of what Mr Trump might see as “terrorism”. That requires tight security cooperation with Israel.
The visit to Washington and the hunger strike have brought into sharp relief the biggest fault line in the Palestinian national movement.
Mr Abbas’s strategy is strictly top-down. Its starting point is that western states – those that have consistently betrayed the Palestinian people over many decades – can now be trusted to help them attain a state.
From this dubious assumption, Mr Abbas has sought to suppress anything that plays badly in western capitals. Pressure has only intensified under Mr Trump.
By contrast, the “battle of empty stomachs” is evidence of a burgeoning bottom-up strategy, one of mass non-violent resistance. On this occasion, the demands are limited to prison reform, but the strike’s impact could spread.
Not least, the model of protest, should it succeed, might suggest its relevance to a Palestinian public disillusioned with Mr Abbas’s approach. They too are living in cells of Israel’s devising, even if larger, open-air ones.
The starkly different logic of these two strategies is harder than ever to ignore.
To stand a hope of winning over the Trump administration, Mr Abbas must persuade it that he is the sole voice of the Palestinians.
That means he must keep a lid on the hunger strike, encouraging it to fizzle out before prisoners start dying and Palestinian fury erupts across the occupied territories. His approach is reported to be creating severe tensions within Fatah.
Wishing only to add to those difficulties, Israeli prime minister Benjamin Netanyahu demanded last week that Mr Abbas halt financial aid to the prisoners’ families, calling it compensation for terrorism.
Mr Abbas also feels compelled to assert himself against his Hamas rivals in Gaza. That is why last week he stopped funding the fuel needed to generate electricity there, having recently cut medical services and salaries to Gaza’s civil servants.
His hope is that, as he turns the screws, Hamas will be toppled or forced to submit to his rule.
But more probably, the fissure with Hamas will deepen, forcing the cornered Islamist movement into another bloody confrontation to break free of Israel’s decade-old blockade. These divisions, most Palestinians increasingly understand, weaken rather than strengthen their cause. Mass non-violent resistance such as the hunger strike, by contrast, has the potential to reunite Fatah and Hamas in struggle, and re-empower a weary Palestinian populace.
Reports have suggested that Mr Barghouti has reached a deal with jailed Hamas leaders committing to just such a struggle in the occupied territories once Mr Abbas has departed.
A popular struggle of non-violence – blocking settlement roads, marching to Jerusalem, tearing down walls – would be hard to characterise as terrorism, even for Mr Trump. It is the Israeli army’s nightmare scenario, because it is the only confrontation for which it has no suitable response.
Such a campaign of civil disobedience, however, stands no chance of success so long as Mr Abbas is there to undermine it – and insists on obediently chasing after illusions in Washington.
Jonathan Cook is an independent journalist in Nazareth