WASHINGTON — President Trump’s post-midterm election news conference at the White House last week took a surprising turn when a reporter asked about locking down his 2020 ticket.
“Mike, will you be my running mate?” Mr. Trump asked Vice President Pence, who stood up, raised his hand, and nodded.
“Will you? Thank you. O.K., good,” the president said. “That was unexpected, but I feel very fine.”
But in private Mr. Trump is apparently not feeling so fine. In recent weeks, with his electoral prospects two years from now much on his mind, Mr. Trump has focused on the person who has most publicly tethered his fortunes to him. In one conversation after another he has asked aides and advisers a pointed question: Is Mike Pence loyal?
Mr. Trump has repeated the question so many times that he has alarmed some of his advisers. The president has not openly suggested dropping Mr. Pence from the ticket and picking another running mate, but the advisers say those kinds of questions usually indicate that he has grown irritated with someone.
The answers Mr. Trump gets to his question have varied, depending on whom he asks.
Within the White House, most people he has talked to have assured the president that Mr. Pence has been a committed soldier, engaging in activities that Mr. Trump has eschewed, such as traveling to Hawaii to receive the remains of veterans of the Korean War, or visiting parts of the globe that Mr. Trump has avoided.
But some Trump advisers, primarily outside the White House, have suggested to him that while Mr. Pence remains loyal, he may have used up his utility. These advisers argue that Mr. Trump has forged his own relationship with evangelical voters, and that what he might benefit from more is a running mate who could help him with women voters, who disapprove of him in large numbers.
Others close to the president believe that asking about Mr. Pence’s loyalty is a proxy for asking about whether the vice president’s chief of staff, Nick Ayers, is trustworthy. Mr. Trump has been considering making Mr. Ayers the White House chief of staff to replace John F. Kelly, the retired Marine general — a decision several White House officials say has been with the encouragement of his adult children. But the president has put off making a decision for now.
The conversations were described in interviews with nearly a dozen White House aides and others close to Mr. Trump. But Hogan Gidley, the deputy press secretary, disputed that Mr. Trump had any misgivings. “The president absolutely supports the vice president and thinks he’s doing an incredible job helping to carry out the mission and policies of this administration.”
Mr. Trump has never completely forgotten that during the 2016 campaign Mr. Pence issued a disapproving statement the day after the infamous “Access Hollywood” tape was made public, on which the president was heard making comments boasting about grabbing women’s genitals.
But Mr. Trump has kept close counsel about whether he is seriously considering making a change to the ticket, or simply poll-testing advisers as the campaign begins. And few advisers believe he would really go through with it.
Veterans of previous White Houses described this type of questioning as a frequent occurrence before a re-election campaign begins in earnest.
“The idea of changing a ticket has been discussed by at least some aides in every White House and it almost never happens,” said Dan Pfeiffer, a former communications director for President Barack Obama.
“I would also say the electoral significance of the vice-presidential nominee is one of the most overrated things in U.S. politics, particularly in a re-election, which is almost always a referendum on the performance of the president,” he said. “Changing the No. 2 is not going to change that.”
In 2012, Mr. Obama’s aides briefly talked about replacing Vice President Joseph R. Biden Jr. with Hillary Clinton for the president’s re-election effort.
In recent weeks, Mr. Pence has stepped into public frays to defend the president, saying that “everyone has their own style” when asked if Mr. Trump’s fiery political and personal language have led to violent acts, including the mass shooting at a Jewish synagogue and bomb threats mailed to prominent Democratic figures.
On other issues, Mr. Pence has staked out a firm position when the president has seemed noncommittal or disengaged.
He has repeatedly vowed consequences for the Saudis over the killing of the dissident journalist Jamal Khashoggi. And before attending the Asia-Pacific summit meeting in Singapore in Mr. Trump’s absence on Wednesday, Mr. Pence forcefully told Myanmar’s leader Aung San Suu Kyi, that political violence that caused more than 700,000 Rohingya Muslims to flee that country was “without excuse.”
On his Asia trip, Mr. Pence has also called for press freedom even as the president continues to assail journalists back home.
The two men speak daily, sometimes multiple times. But some of Mr. Trump’s advisers believe that the dynamic between the president and Mr. Pence has changed in the first two years of Mr. Trump’s term, part of a pattern in many of Mr. Trump’s relationships.
Some of Mr. Trump’s outside advisers have mentioned Nikki R. Haley, the United States ambassador to the United Nations, a post she plans to leave at the end of the year, and former governor of South Carolina, as a potential running mate. Ms. Haley is close with Mr. Trump’s daughter, Ivanka Trump, and his son-in-law, Jared Kushner, and Mr. Trump gave her an unusually warm send-off in the Oval Office when she announced she was leaving the United Nations job in September.
And Ms. Haley on the ticket might help Mr. Trump win back the support of the women voters, who voted for Democratic candidates in large numbers in the midterm elections.
But Ms. Haley is less likely to show the same kind of public loyalty as Mr. Pence, a former congressman and governor of Indiana. She recently poked fun at Mr. Trump in a speech at the annual Al Smith Dinner in New York City, where politicians historically make jokes at the expense of themselves and their supporters. And that was after her original speech was toned down, and some of the barbs at Mr. Trump removed, people familiar with the address said.
Some of Mr. Trump’s evangelical supporters feel particularly strongly that making a change would be a mistake.
“Mike Pence is an invaluable asset to President Trump politically, on shaping policy and personnel, and in cementing the epoxy-like bond with evangelicals,” said Ralph Reed, the founder of the Faith and Freedom Coalition. “He is also fiercely loyal, which is the coin of Trump’s realm. The president has said he plans to keep Pence, and that is an infinitely wise decision.”
But some who have studied evangelical voters and their political activity say losing Mr. Pence wouldn’t necessarily be a disaster.
Robert P. Jones, the chief executive of the nonpartisan Public Religion Research Institute, said that the president faced an “at best moderate risk” if he were to drop Mr. Pence from the ticket.
Mr. Jones said that while Mr. Pence may have served as a validating figure for white evangelicals, recent research showed that 7 out of 10 white evangelicals who identify with or lean toward the Republican Party would prefer Mr. Trump over any alternative Republican candidate in 2020.
A third of white evangelicals who support Trump, Mr. Jones said, indicated there was virtually nothing the president could do to shake their trust — which theoretically includes selecting a new running mate.
“At the end of the day evangelicals have become sold not just on Pence but on Trump himself,” Mr. Jones said.