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In a video released Wednesday to promote her upcoming book, Hillary Rodham Clinton warned that the nation must “deal with the cancer of inequality.” Days earlier, she said the country is facing another “Gilded Age of the robber barons” and rattled off statistics about the financial gap between rich and poor.

The comments mark a new populist emphasis for Clinton, who is seeking to tamp down growing criticism from the left about her husband’s economic policies in the 1990s. The issue could become a serious political headache for Clinton as she considers a presidential run in 2016, raising the possibility of a challenge from the left on free trade, bank regulation and other populist causes.

How Clinton navigates economic issues could help determine how successful she would be as a candidate, particularly given her fraught history with the left wing of the Democratic Party. Her Senate vote in 2002 to authorize the Iraq war caused an irreparable rift with liberals in her 2008 presidential bid — one that was exploited by her up-and-coming Democratic primary rival, Barack Obama.

During her first White House bid, the booming Clinton economy of the 1990s was considered a political asset. But many liberals have since soured on parts of that record, arguing that Clinton administration policies contributed to the 2008 financial crash, the Great Recession and the economic malaise that followed.

Critics say Bill Clinton’s support for free trade agreements destroyed millions of middle-class manufacturing jobs, while his hands-off approach to financial regulation laid the groundwork for the financial crisis. Economic inequality soared during the 1990s, exacerbated by Clinton’s support of tax cuts on investment income.

Since then, Bill and Hillary Clinton and their advisers have maintained close ties to Wall Street — another major point of tension with progressives.

“I think a choice will have to be made by Mrs. Clinton as to how close she is going to be to Wall Street and big business — not only in terms of campaign contributions but also even more importantly in terms of policies,” said Robert Reich, a prominent liberal and close adviser to Bill Clinton in the 1990s. “That is the question progressive Democrats will really focus on.”

The enthusiastic response on the left to Sen. Elizabeth Warren (Mass.), who has championed an anti-Wall Street message, underscores the challenge facing Clinton. Although Warren denies any interest in running for president, liberal Democrats are clamoring for her to do so. And Vice President Biden — another potential 2016 candidate — told a group of Democrats recently that the nation’s middle-class struggles began in the latter years of the Clinton administration.

The Clintons have begun providing clues to how they will respond to the economic critiques. In a series of speeches, they have continued to herald the 1990s as a model, while also focusing on contemporary concerns about inequality and the frustrations of millions of Americans in getting well-paying jobs.

“Instead of getting ahead, they’re finding it harder than ever to get their footing in our changing economy,” Hillary Clinton said in a speech this month at the centrist New America Foundation think tank. “The dream of upward mobility that made this country a model for the world feels further and further out of reach, and many Americans understandably feel frustrated, even angry.”

She added, “The 1990s taught us that even in the face of difficult long-term economic trends, it’s possible, through smart policies and sound investments, to enjoy broad-based growth and shared prosperity.”

Sprinkling her remarks with statistical references and the research of prominent economists, Clinton echoed points that President Obama has made often over the past several years. But she also connected the nation’s big economic questions to her personal narrative — the line of women in her family or her own work on child opportunity when she was a law student.

“On economic issues, she has a long history on these topics that are in her voice,” said Neera Tanden, the president of the Center for American Progress and a longtime policy adviser to Clinton. “She has a long record of talking about these very issues, and she had a perspective that if we don’t grow the economy for everyone, it’s not going to be good for anybody.”

Clinton’s supporters also argue that she can’t be expected to be held responsible for the policies of her husband. But many liberals say she must reject those they find most objectionable.

The liberal critique often begins with the Clinton administration’s positions on two issues: trade and financial regulation. In the 1990s, Bill Clinton strongly supported the North American Free Trade Agreement and deeper trade ties with China. He also agreed to demolish the wall separating investment and commercial banking, while blocking a proposal to regulate the exotic financial instruments known as derivatives.

Much of his thinking was guided by his Treasury secretary and adviser, former Goldman Sachs chairman Robert Rubin, whose brand of market-friendly “Rubinomics” gave rise to a cadre of Democratic policymakers who have long dominated the party.

In the view of many liberals, trade caused deep job losses in the nation’s manufacturing sector, while deregulation helped sow the seeds of the financial crisis. Such worries scuttled the nomination of Rubin’s successor as Treasury secretary, Lawrence H. Summers, to be Federal Reserve chairman last year.

It also has become clear in recent years that inequality continued to soar during the 1990s. According to widely respected academic research, the share of national income for the top 1 percent of earners increased from 13.5 percent in 1992 to 16.5 percent by 2000 — more than the increase registered from 2001 through 2012.

Today, leading liberals say Hillary Clinton must make clear how she will differentiate herself from the perspectives that shaped economic policy in the 1990s.

“Whatever the intentions were, when you look back, there was not enough done on the worker-wage side of the equation,” said Andy Stern, former president of the Service Employees International Union. “I don’t think anyone doubts the ability of [Hillary Clinton] to work with the Wall Street part of the Democratic Party. She’s going to have to put her foot squarely on the side of Main Street.”

Roger Hickey, founder of the liberal Campaign for America’s Future, said “we hope she’s a different person” now.

“That’s the question,” he continued. “Is Hillary going to run and govern if she’s elected on the basis of that administration that she was a part of, or has she changed in anyway?”

Longtime advisers to the Clintons say it’s unfair to cherry-pick the Clinton legacy or to assume that the former New York senator will look at the world in the same way that her husband did two decades ago.

A briefing document recently assembled by Bill Clinton’s staff noted that during his administration, the poverty rate dropped from 15.1 percent in 1993 to 11.3 percent in 2000, while median family income reached its historic peak in 1999.

Income among the poorest 20 percent of Americans also increased faster than the top 20 percent of Americans, the document said — a point the former president has made repeatedly in recent speeches.

“President Clinton isn’t recasting his case, he is just restating it,” said Gene Sperling, a longtime economic adviser who is close to the Clintons. “The goal is not finding the right label, but the right recipe that leads to shared economic growth for the middle class and the working poor. And it is undeniable that both groups shared in broad-based income growth during most of his tenure.”

Rob Shapiro, another Clinton economic adviser from the 1990s, said Hillary Clinton will find her own way because the economy is much different now.

“Hillary has got to address a very different set of problems than Bill has got to address,” he said. “Inequality is enormously greater than it was in 1992. That has become an independent issue that just didn’t exist then as a public issue.”