Jeremy Shapiro, a former State Department official who is the director of research for the European Council on Foreign Relations, said that Mrs. May had to be careful because Mr. Trump almost never has fights with someone in the room.
“Then you think that maybe this isn’t the person I thought he was, but 48 hours later he tweets something and disappoints you,” he said.
Mrs. May may be aware that she is a supplicant, Mr. Shapiro said, “but Trump has her boxed up in her domestic politics — the problem of Farage, her need to control the Brexit wing of her party and her need to fashion a Brexit that won’t destroy her prime ministership.”
Mr. Trump has made reference to the warm, vital relationship between President Ronald Reagan and Margaret Thatcher. “But they were an actual team, they actually worked together, and Trump can’t stand that,” Mr. Shapiro said.
Mr. Freedland said that the Reagan-Thatcher connection mattered, “because there was extra leeway and space for both of them, because of the personal relationship.”
The new president, Mr. Shapiro suggested, will see Mrs. May’s desire to meet him first as a sign of weakness. “There’s no way Trump will say it that way face-to-face, but later it will come through in the relationship and in any U.S.-U.K. trade deal,” which he expects will not be particularly favorable to Britain.
For Mr. Trump, he suggested, those leaders who do not ask for early meetings are the ones who show the most strength.
Mr. Meyer, the former ambassador, is less concerned. “She’s completely aware of the dangers, and I think she might turn out to be a bit of an iron lady in some of what she says,” he said. “She won’t sound like a supplicant. But getting the balance right between saying all the oleaginous things about the special relationship and saying the things that matter to us will be the key.”
Mrs. May also addressed Republicans in Philadelphia on Thursday at their annual retreat, which Mr. Trump also attended, before meeting him at the White House on Friday afternoon. Then she flies to Ankara, Turkey, for a meeting with President Recep Tayyip Erdogan.
On issues of trade, terrorism, migration, security, NATO and Cyprus, Mrs. May’s spokeswoman said, Turkey, too, “is such an important partner.”
Mr. Trump has emphasized his affection for Britain and for Brexit by returning a bust of Winston Churchill to the Oval Office.
Mr. Obama’s replacement of the bust by one of Martin Luther King Jr. became an issue in Britain before Brexit, with the current foreign secretary, Boris Johnson, claiming that Mr. Obama removed the Churchill bust because he “is a symbol of the part-Kenyan president’s ancestral dislike of the British Empire.”
As a personal gesture after Christmas, Mrs. May sent Mr. Trump a copy of Churchill’s famous speech to the American people on Christmas Eve 1941, weeks after Japan’s attack on Pearl Harbor brought the United States into the war.
In her letter, she told Mr. Trump that “the sentiment” Churchill had expressed — “of a sense of unity and fraternal association between the United Kingdom and United States — is just as true today as it has ever been.”
Maybe. Maybe not.