Shaul Arieli, an Israeli expert on political geography who prepared maps for past negotiations with the Palestinians and is a member of Commanders for Israel’s Security, the group behind the billboard campaign, said “one state is impossible” for Israel. Demographically and economically, absorbing millions of comparatively poor Palestinians would destroy it, he said.
Results of a survey of Israelis and Palestinians released on Thursday, put out jointly by Tel Aviv University and Israeli and Palestinian research centers, indicated that 55 percent of Israelis still support the notion of a two-state solution, while support among the Palestinians dropped to 44 percent. But the numbers on both sides rose significantly when they were offered additional incentives like a broader regional peace between Israel and the Arab world. Among Palestinians, support rose for the ability to work freely in Israel even after the establishment of an independent state. The survey included a representative sample of 1,270 Palestinians and 1,207 Israelis.
Israelis are increasingly fearful of the prospect of a Palestinian state at their doorstep. They see other areas of the Middle East in chaos. After Israel unilaterally left the Gaza Strip in 2005, they watched as the militant group Hamas, which rejects Israel’s existence, seized full control of the territory after winning legislative elections. And they know that without the West Bank, Israel is just nine miles wide at its narrowest point.
There is also the emotional issue for those who identify the West Bank as the heart of the biblical Jewish homeland promised by God.
The Israeli idea of Palestinian statehood never included all of the attributes of full sovereignty. Israel insists on a demilitarized state, and Mr. Netanyahu says the Israeli military has to keep overall security control.
Together with other so-far-intractable issues — like the fate of Jerusalem and of Palestinian refugees — many experts have long said that the maximum Israel can offer does not meet the minimum Palestinian requirements.
Saeb Erekat, a senior Palestinian official, noted this week that the two-state solution “represents a painful and historic Palestinian compromise of recognizing Israel over 78 percent of historic Palestine.”
President Mahmoud Abbas of the Palestinian Authority, an interim government that has held sway in parts of the West Bank since the 1990s, is weakened by internal struggles and threatened by his rivals in Hamas.
Mahmoud Zahar, a hard-line member of Hamas and one of its founders in Gaza, said of Mr. Abbas in an interview this week: “He is wasting his time. He is wasting our time and helping the Israelis expand settlements. He is a traitor. He is a spy.”
When the former United States secretary of state, John Kerry, came up with a proposed framework accord defining the principles of a comprehensive two-state agreement after months of negotiations in 2014, Mr. Abbas did not respond.
Since then, Israel has approved plans for thousands of new settler homes in the West Bank and East Jerusalem and has moved to retroactively legalize settler outposts that were built throughout the territory. The measures have further entrenched the occupation, now in its 50th year since Israel captured the territory from Jordan in the 1967 war.
A growing number of right-wing Israeli ministers, including from Mr. Netanyahu’s Likud Party, are pushing to annex the settlements that Israel intends to incorporate within its borders under any future deal. Israel has also invested heavily in roads and infrastructure connecting and serving the West Bank settlements, now home to some 400,000 people.
Yet supporters of the two-state solution insist it still could be executed.
Both sides have recognized that it would require adjustments along the 1967 lines. Mr. Arieli, the political geographer, said Israel could keep 80 percent of its West Bank settlers within its borders by swapping territory equal to about 4 percent of the West Bank. Many of the remaining 20 percent of settlers — roughly 30,000 families — would most likely agree to move back into Israel for compensation, he said.
The numbers can also be deceptive, and some experts insist that much of the change on the ground in recent years can be reversed.
About 50 percent of the growth of the settler population has come in two large ultra-Orthodox settlements, Modiin Illit and Beitar Illit. Both are considered swappable, being close to the 1967 line. Jews mostly went there for cheap housing, not ideology. Together, these two settlements have about 130,000 residents — a third of the total settler population of the West Bank.
In some more outlying settlements, Mr. Arieli said, the population was decreasing as Israelis were “voting with their feet” by not moving in, or moving out. Settlement leaders attribute the drop to pressure from the Obama administration that limited the construction of new homes.
Mr. Khatib, of Birzeit University, agreed that a two-state solution was still physically possible “with some creativity, like swapping.” But, he said, “It won’t remain so for long.”
What is lacking is political will of the leaders on both sides.
Nahum Barnea, a leading Israeli columnist, wrote in the newspaper Yedioth Ahronoth on Thursday that if Mr. Trump were “slightly more informed,” he might have realized that it was not an issue of one state or two states: “The two sides, in practice, have chosen a third option: not to agree.”