Israel's neoconservative cheerleaders in Washington who reportedly leaned on Mubarak in 2007, during George W Bush's presidency, are now influencing Middle East policy again in the Trump administration.
And although Sisi appears to have stood his ground in 2014, subsequent dramatic changes in the region are likely to have weakened his hand.
Both Abbas and Hamas are more isolated than ever, and the situation in Gaza more desperate. Israel has cultivated much closer ties to the Gulf states as they fashion joint opposition to Iran. And the Trump administration has dropped even the pretense of neutrality in resolving the Israeli-Palestinian conflict.
In fact, Trump's Middle East team led by Kushner adopted from the outset Israel's so-called "outside-in" paradigm for arriving at a peace agreement.
The idea is to use a carrot-and-stick approach -- a mix of financial inducements and punitive sanctions -- to bully Abbas and Hamas into making yet more major concessions to Israel that would void any meaningful moves towards Palestinian statehood. Key to this idea is that Saudi Arabia and the United Arab Emirates can be recruited to help Israel in its efforts to force the Palestinian leadership's hand.
Egypt, current reports indicate, has come under similar pressure from the Gulf to concede territory in Sinai to help Trump with his long-delayed "deal of the century."Muslim Brotherhood threat
Sisi and his generals have good reason to be reluctant to help. After they grabbed power from Morsi's Muslim Brotherhood government, they have done everything possible to crush homegrown Islamist movements, but have faced a backlash in Sinai.
Hamas, which rules Gaza, is the sister organisation of the Muslim Brotherhood. Egypt's generals have worried that opening the Rafah border crossing between Sinai and Gaza could bolster Islamist attacks that Egypt has struggled to contain. There are fears too in Cairo that the Sinai option would shift the burden of Gaza onto Egypt's shoulders.
This is where Trump and Kushner may hope their skills at wheeler-dealing can achieve a breakthrough.
Egypt's susceptibility to financial inducements from the Gulf were on display last year when Sisi's government agreed effectively to sell off to Saudi Arabia two strategic Red Sea islands, Tiran and Sanafir. They guard the entrance to the Gulf of Aqaba and the Suez canal.
In return, Egypt received billions of dollars in loans and investments from the kingdom, including large-scale infrastructure projects in Sinai. Israel reportedly approved the deal.
Analysts have suggested that the handover of the islands to Saudi Arabia was intended to strengthen security and intelligence cooperation between Israel, Egypt and Saudi Arabia in dealing with Islamic militants in Sinai.
This now looks suspiciously like the prelude to Trump's reported Sinai plan.Over the Palestinians' heads
In March, the White House hosted 19 countries in a conference to consider new ideas for dealing with Gaza's mounting crisis. As well as Israel, participants included representatives from Egypt, Jordan, Saudi Arabia, Qatar, Bahrain, Oman and the United Arab Emirates. The Palestinians boycotted the meeting.
Much favored by the Trump team was a paper delivered by Yoav Mordechai, an Israeli general and key official overseeing Israel's strategy in the occupied territories. Many of his proposals -- for a free trade zone and infrastructure projects in Sinai -- are now being advanced.
Last month Kushner visited Saudi Arabia, Qatar, Egypt, and Jordan to drum up support. According to interviews in the Israel Hayom daily, all four Arab states are on board with the peace plan, even if it means bypassing Abbas.
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