There was little of the public dissent that hobbled his predecessor, Theresa May, when she undertook similar negotiations — a sign that Mr. Johnson might be on the cusp of a major step to settle Britain’s three-year national drama over Brexit.
But even if he produces an 11th-hour success, analysts said, Mr. Johnson could face a familiar conundrum in London: If he gives too much ground to Brussels on the Northern Ireland border, he will not be able to win backing for the agreement from key elements of his coalition in Parliament.
“There is a robust trade-off here,” said Mujtaba Rahman, a former European Commission economist now at the Eurasia Group, a political risk consultancy, and one of the people briefed. “Technically, the deal can be done, but can the politics deliver?”
Rory Stewart, a former cabinet minister and one of 21 lawmakers purged from the Conservative Party by Mr. Johnson over Brexit policy, was more pessimistic. “I don’t think he’ll get anything,” he said.
On the off chance that he succeeds, Mr. Stewart said, “the deal that he will get will be significantly worse than the withdrawal agreement,” referring to the treaty negotiated by Mrs. May. That would leave Britain facing an economic hit and could dissuade lawmakers from supporting any new agreement.