Skepticism abounds, especially among those who spent years struggling to overcome the same challenges with the same set of tools. President Barack Obama and his advisers debated for months putting forth their own parameters for a deal, ultimately outlining a general set of principles at the end of last year in a speech by Secretary of State John Kerry as time ran out on the administration.

“There’s nothing new under the sun when it comes to Middle East peace,” said Philip Gordon, a White House Middle East coordinator under Mr. Obama. “When you get into these details, that’s when you come up against the strong objections of the two sides. If they don’t want it to be dead on arrival, they may wind up with vague principles, but as we’ve seen, even vague principles are beyond what the parties are willing to embrace.”

Tamara Cofman Wittes, a State Department official under Mr. Obama, said both Israeli and Palestinian leaders “are heavily constrained” not only by their own governing coalitions but by suspicious and risk-averse publics. “It’s hard even for willing political leaders to make major concessions under those circumstances,” she said.

The core four-member team drafting the plan includes Mr. Kushner, Mr. Greenblatt, Dina H. Powell, a deputy national security adviser, and David M. Friedman, the ambassador to Israel. They are consulting with Donald Blome, the consul general in Jerusalem, and others from the State Department and National Security Council. Officials said the effort may take until early next year.

Mr. Trump and his team make no bones about being pro-Israel. The president has boasted of being Israel’s “biggest friend” and Mr. Kushner, Mr. Greenblatt and Mr. Friedman are all Orthodox Jews with ties to Israel. But Ms. Powell is an Egyptian-born Coptic Christian and Mr. Kushner has developed strong ties with the Saudis and other Arabs and recently returned from a visit to Riyadh. Mr. Trump has met with Mr. Netanyahu and Mr. Abbas three times each.

The team has drawn praise from across the spectrum. “We do believe this is a historic opportunity, and we will spare no effort to support President Trump’s investment in a better future,” Husam Zomlot, the Palestinian Authority’s envoy to Washington, said in an interview. During a trip to London this month, Mr. Netanyahu said, “They are trying to think out of the box.”