Surrounded by staff, former secretary of state Hillary Rodham Clinton signs her new book, “Hard Choices,” at the Union Square Barnes & Noble in New York on Tuesday. (Melina Mara/The Washington Post)

CHICAGO — Hillary Rodham Clinton was a popular first lady, a respected senator and an admired secretary of state.

But the first 24 hours of her campaign-like book tour this week served as a reminder that Candidate Clinton has never been as sharp and polished as many of her boosters might hope.

Clinton stumbled out of the gate by saying in a television interview that she and her husband were “dead broke” when they departed the White House in 2001 and had “struggled” to pay mortgages on their two multimillion-dollar houses. The gaffe came in defense of her $200,000-a-pop speaking fee — which her interviewer, ABC News anchor Diane Sawyer, noted was five times the median family income.

Technically, Clinton was correct. She and Bill Clinton had debts as high as $10.6 million, according to their federal financial disclosure in 2000. But her remarks struck many political observers as tone deaf amid rising concern over income inequality.

On Tuesday morning, Clinton tried to correct her misstep.

“Let me just clarify that I fully appreciate how hard life is for so many Americans today,” Clinton said on ABC’s “Good Morning America.” “It’s an issue that I’ve worked on and cared about my entire adult life. Bill and I were obviously blessed. We worked hard for everything we got in our lives and we have continued to work hard.”

Clinton’s allies acknowledge that, if she runs, one of her greatest challenges will be crafting a message that addresses the populist economic currents coursing through the Democratic Party and offers hope to the many voters who feel left behind in President Obama’s economic recovery.

Yet the optics surrounding Clinton’s book tour so far have reinforced the rarefied life she now leads.

Arriving Tuesday at a Barnes & Noble in New York for her first book signing, Clinton was whisked inside by her Secret Service detail while supporters who waited hours in line to meet her were handed notices with eight strict rules, including: “She will not be personalizing the book or signing memorabilia. NO posed photography with the author.”

Inside the store, Clinton gave brief remarks, posed with her book, “Hard Choices,” and settled into a leather chair to sign hundreds of copies. She took no questions and did not give a reading. But she did greet her supporters with a smile.

Carina Cappello, a college student majoring in political science, took advantage of her time with Clinton to pose the question many in line wanted answered. After reading that Clinton would run for president if she felt that she had the vision and capability to lead America, Cappello said she asked the would-be candidate, “Do you think you have the vision and capability?” Clinton replied, “If I decide to run, yes.”

From there, Clinton jetted to Chicago, where she delivered a paid speech to a joint meeting of the Food Marketing Institute and the United Fresh Produce Association. Convention officials would not disclose her fee. Former president Bill Clinton also gave a paid speech on Tuesday, at the Insurance Accounting and Systems Association in Indianapolis.

Republicans, who have feared the potential of a Clinton candidacy in 2016, said her remarks this week about her wealth and the struggles of the middle class show she is the same Clinton they remember from 2008: conventional, calculating and struggling to connect with voters.

“I think it’s even more clear that she’s running, but it’s also very clear that she hasn’t improved at all as a candidate since 2008,” said Kevin Madden, a strategist who helped 2012 GOP nominee Mitt Romney recover from many missteps talking about his wealth.

Tim Miller, executive director of America Rising, a super PAC leading GOP attacks on Clinton, said that “people are being reminded of the fact that her political skills are not at the level of her reputation.”

Miller said Clinton’s and her husband’s paid speeches and appearances — particularly those at big Wall Street banks — are a vulnerability that Republicans can exploit in 2016. “When do they stop selling themselves?” he asked. “When you run for president, you’ve eventually got to take down the ‘For Sale’ sign.”

Clinton’s allies rushed to her defense, saying strengthening the middle class has been a cause of Clinton’s life — from her work out of law school for the Children’s Defense Fund to her current role at the Bill, Hillary and Chelsea Clinton Foundation.

“The Republicans are threatened by her, so they’re going to pick apart every single word she says in an effort to take her down,” said former Michigan governor Jennifer Granholm (D). “Why are these books flying off the shelves? Why does she have people lined up overnight waiting to see her? Because she represents hope for their future.”

But it’s not only Republicans who have seized upon Clinton’s gaffe to portray her as out of touch. Former Montana governor Brian Schweitzer, who is considering a Democratic primary challenge, said in an interview that he thinks Clinton’s speaking fees will become a “turbocharged” issue with middle-class voters.

“Does the guy that works in a steel mill begrudge somebody who can get $300,000 for 30 minutes when he’s making $20 an hour and when he adds up his mortgage and his car payments and his college education for his three kids, and gets to the end of the month and calls himself ‘flat broke’ too?” Schweitzer said.

He added, “I’ve been to Iowa, I’ve been to New Hampshire and I’ve been to South Carolina. People there, they build things, they grow things, they fix things . . . I don’t think folks in those states or 47 other states really understand this notion that you can be paid without producing anything.”

Joe Lockhart, a former Clinton White House press secretary, cautioned against drawing any broad conclusions about Clinton’s political strength or ability to connect with average Americans.

“The conclusion that I would draw is that when you’re doing loads and loads of interviews, sometimes things just don’t come out of your mouth the way you intend them to,” Lockhart said. “I don’t see this as more than something that we sit around and talk about for 24 hours.”

Philip Bump in New York contributed to this report.