Mr. Juncker, who believes that the backstop is actually favorable to Britain, is apparently offering commitments to finish a future relationship in good time so that the backstop is never needed. He has previously talked of wording to make it clear that Brussels dislikes the backstop, too, and would endeavor to ensure that if triggered, it would not last long.

Margaritis Schinas, Mr. Juncker’s spokesman, said that Mrs. May had “raised various options” for getting around the backstop arrangement, but he provided no details. European Union negotiators have said that they can work to have most customs checks in ships and factories, not on the border itself, but that no technical fix was currently available to remove the need for the backstop.

Analysts scoffed at the notion that Mrs. May could present some new, paradigm-shifting proposal that might propel the negotiations forward.

“Theresa May has said she is looking for new ideas, but doing so 50 days before the deadline when you have had almost 1,000 days to negotiate is not credible,” said Simon Fraser, former head of Britain’s foreign office, now managing partner at Flint Global, a consultancy.

Most European officials believe that the risks of leaving without ratifying a withdrawal agreement — known as “no-deal Brexit” — are higher for Britain than for continental Europe and that if Mrs. May were to pursue that course, Parliament would step in, seize control of the process and seek to postpone the exit date. So they have every incentive to let things play out in London first before making their move.

“I don’t think they will give her anything until they know clearly what her proposal is,” Mr. Fraser said. “They will want to give once and they will only want to give when it is clear that it is going to solve the problem, and none of those three conditions are so far satisfied.”

Certainly there was little sign of movement on Wednesday, when both Donald Tusk, president of the European Council, and Leo Varadkar, the Irish prime minister, restated their commitment to the backstop.