NASHVILLE — Mayor Megan Barry, the first woman to lead this city, has been the kind of politician who seemed to effortlessly reflect the tenor of her place and time. Like others in booming Nashville, she is an ambitious transplant, socially liberal but business-friendly, a non-Southerner comfortable in a Southern context. It is a formula that has earned her poll numbers that would be the envy of any politician.
But in recent days, scandal has threatened to dim one of the Democratic Party’s brightest Southern stars. And though many residents of Nashville, a bastion of social liberalism in a deeply conservative state, have been willing to dismiss with a kind of Gallic shrug her admission of a monthslong extramarital affair with the police officer leading her security detail, other aspects of the episode are mounting, leading some here to wonder how long she can hang on.
Ms. Barry, 54, a former corporate ethics and compliance officer who became mayor in September 2015, announced the affair at a somber and apologetic news conference last Wednesday, and insisted that it was over.
“I am embarrassed and I am sad and I am so sorry for all the pain that I have caused my family and his family,” she said, referring to former Sgt. Robert Forrest Jr. of the Metro Nashville Police Department, who is also married and who retired from the force at the end of last month. “And I know that God will forgive me — but that Nashville doesn’t have to.”
In a brief interview Sunday night, Ms. Barry, amid swirling rumors that she might resign, said she had no plans to do so. “No, no, no,” she said.
But still lingering are questions about numerous taxpayer-funded city business trips Ms. Barry took with Mr. Forrest, raising the possibility of bruising weeks ahead for the mayor. The Tennessean newspaper, citing public records, reported that the pair took some trips in the company of other city officials, but that nine trips, including one to Athens, Greece, were taken by Ms. Barry and Mr. Forrest alone.
The Tennessee Bureau of Investigation, at the request of Nashville District Attorney General Glenn R. Funk, is looking into whether Ms. Barry or Mr. Forrest broke any laws by misusing public funds. The City Council, generally supportive of the mayor’s agenda, voted on Tuesday to create a special committee to investigate the trips.
Ms. Barry has said that she did nothing wrong. A lawyer for Mr. Forrest declined to comment Tuesday.
This week, The Tennessean also reported that Ms. Barry had recommended Mr. Forrest’s adult daughter, Macy Amos, for an entry-level job that Ms. Amos later landed in the city law department.
Sean Braisted, the mayor’s spokesman, acknowledged that Ms. Barry recommended Ms. Amos to the city law director sometime after she took office. But Mr. Braisted insisted that the recommendation, and Ms. Amos’s first day of work, all predated the affair, which he said started sometime in the spring of 2016.
“Ms. Amos was recommended by many people inside and outside of Metro Government,” Mr. Braisted said in a prepared statement. “She began the interview process with the Department of Law in December of 2014. She was offered a position in 2015 by Metro Law Director Jon Cooper and began her job in 2016.”
The scandal has dealt an unexpected jolt to a political narrative here of a mayor well-matched with her city’s burgeoning self-conception as a sophisticated but down-home place, where honky-tonks, high-rises and, increasingly, a pronounced streak of social liberalism all coexist.
As a City Council member, Ms. Barry had been an outspoken champion of abortion rights and same-sex marriage. In a September 2015 runoff election, she defeated David Fox, a former hedge-fund manager. Mr. Fox tacked to Ms. Barry’s right, but his strategy seemed to show that the culture-war dog did not hunt in the new Nashville. Voters shrugged off his campaign’s assertion, in radio advertisements, that Ms. Barry and her husband, Bruce Barry, an American Civil Liberties Union member, had opposed prayer before high school football games.
In interviews this week, a number of liberals and conservatives said they did not wish to judge Ms. Barry’s decisions in her private life. But many of them said the questions about the money and the trips concerned them.
“With two consenting adults, I understand that those things happen,” said James R. Dickson III, 51, an insurance broker and Republican who was having a drink at Sperry’s Restaurant, a clubby, old-school haunt in the well-heeled Belle Meade area. “My issue is the financial piece of it.”
The sentiment was echoed almost exactly by Khadija Ali, 21, a socially liberal college student who was hanging out Monday at Bongo Java, a popular coffee shop in Ms. Barry’s bourgeois-bohemian neighborhood of Belmont/Hillsboro Village.
The problem was not Ms. Barry’s personal life, she said, but the question of whether public funds might have been misused. “Then it becomes an issue,” she said.
The issue of Ms. Barry’s gender has also manifested itself in complicated ways. “I wonder if our mayor was a man, if the press coverage would be so gentle,” a resident named Ken Witt wrote in a letter to The Tennessean. “I think there would be pressure for an immediate resignation!”
But Carly Blaine, 22, a liberal activist and student at Belmont University, said that Ms. Barry crossed an ethical line when she engaged in an affair with a subordinate. It does not matter, Ms. Blaine argued, whether a person who engages in such an affair is a male or a female.
“Even though it’s a consensual relationship, that’s still an abuse of power,” Ms. Blaine said. Referring to the #MeToo movement, she added: “There’s a huge movement going on right now.”
A Vanderbilt University poll last year showed that Ms. Barry enjoyed a 72 percent overall approval rate. Her successes have included a popular youth employment program, Opportunity Now, and the landing of a Major League Soccer team.
But some African-American leaders have criticized her handling of budget problems at Nashville’s public hospital. And Black Lives Matter activists have criticized her for the city’s handling of a police shooting of a 31-year-old black man, in which the officer was not prosecuted.
This week, an activist group called Community Oversight Now raised the possibility that high-ranking police officers may have wielded knowledge of the affair to influence the mayor’s decisions on police reform issues. (In a statement, Mr. Braisted said that Ms. Barry took her positions on such issues “in the best interest of the entire community.”)
The group’s suspicions may be little more than a conspiracy theory, but they show how difficult it may be for Ms. Barry to maintain what have been deep stores of good will among Nashvillians. It was a bond cemented by tragedy in July, when Ms. Barry announced that her only child, Max Barry, 22, had died of a drug overdose.
His visitation was attended by thousands of locals.
Today, the centerpiece of Ms. Barry’s public agenda may be most imperiled: a multibillion-dollar transit plan that would introduce a light-rail system to the congested city. Voters could consider the plan in a referendum as early as May 1.
Opponents have argued that it is too costly, and a poor match for Nashville’s infrastructure needs.
Until now, the opposition has largely refrained from tying the affair to the transit issue. But on Monday, John Cooper, an at-large councilman who has criticized the transit plan and other big projects backed by the mayor, said he had received numerous calls and emails from constituents expressing “great concerns” about Ms. Barry’s conduct.
“We can’t be too cool to take that seriously,” Mr. Cooper said. “Nashville is kind of proud of being a cool city. We’re cool, and have pretty progressive attitudes on a lot of stuff.”
He added: “It’s heartbreaking for the families involved. But this does speak to trustworthiness, judgment and misuse of money.”