WASHINGTON — When Hillary Rodham Clinton said this month that she was once “dead broke,” it was during an interview in which she led ABC News anchor Diane Sawyer through her $5 million Washington home, appointed like an ambassador’s mansion. Mahogany antiques, vibrant paintings and Oriental rugs fill the rooms. French doors open onto an expertly manicured garden and a turquoise swimming pool, where Clinton recently posed for the cover of People magazine.

On her current book tour, she has traveled the country by private jet as she has for many of her speaking engagements since stepping down as secretary of state last year. Her fee is said to be upward of $200,000 per speech; the exceptions tend to be black-tie charity galas, where she collects awards and catches up with friends such as designer Oscar de la Renta and Vogue editor Anna Wintour.

Such scenes reveal a potentially serious political problem for Clinton as she considers a 2016 presidential run: She and her husband are established members of the 1 percent, leading lives far removed from the millions of middle-class voters who swing elections.

Clinton has underscored the contrast with a series of stumbles in discussing her finances – the latest in an interview with Britain’s Guardian newspaper published Sunday, in which she compared herself with other multimillionaires. Unlike the “truly well off,” Clinton said, she and former president Bill Clinton “pay ordinary income tax” and have amassed their fortune “through dint of hard work.”

Some influential Democrats – including former advisers to President Barack Obama – said in interviews last week they fear that Clinton’s personal wealth and rarefied, cloistered lifestyle could jeopardize the Democratic Party’s historic edge with the middle class.

“I don’t know whether it’s just that she’s been ‘Madam Secretary’ for so long, but she’s generating an imperial image,” said Dick Harpootlian, who recently stepped down as Democratic Party chairman in South Carolina, which hosts an early presidential primary.

Harpootlian, who backed Obama in 2008 and is a longtime ally of Vice President Joe Biden, added: “She’s been living 30, going on 40 years with somebody bringing your coffee to you every morning. Is it more ‘Downton Abbey’ than it is America?”

Multiple Obama campaign advisers – who spoke only on the condition of anonymity – said they fear Clinton’s financial status could hurt her as it did Republican nominee Mitt Romney, whom Obama portrayed in 2012 as an out-of-touch plutocrat.

“It’s going to be a massive issue for her,” one Obama adviser said. “When you’re somebody like the secretary of state or president of the United States or first lady, you’re totally cut off from normal activity, so your perception of the middle-class reality gets frozen in a time warp.”

Asked what Democrats should do, the adviser said: “Panic.”

Clinton’s allies, however, strongly dispute suggestions that she is disconnected from the concerns and values of middle-class Americans. They note she grew up in a middle-class suburb of Chicago and said she has committed her adult life to lifting up the downtrodden – from her early work at the Children’s Defense Fund to initiatives at her family’s charitable foundation.

“The Clinton history has always been how to bring more people into the middle class,” said Robert Zimmeran, a member of the Democratic National Committee from New York.

Bill Clinton rose from poor beginnings in rural Arkansas to the presidency. In 1992, it was Clinton’s everyman connection that helped him defeat then-president George H.W. Bush, a patrician who was ridiculed for not knowing the price of a gallon of milk.

Now Hillary Clinton risks a similar caricature. On tour this month for her new book, “Hard Choices,” Clinton mingled with regular people at signings, but only under strict rules: no photographs and no personalized autographs. There are Secret Service agents to keep the crowds in order and aides to hand her books, count how many she signs and ferry her to the next stop. The former first lady recently said she hasn’t driven a car since 1996.