WASHINGTON — When a dozen protesters in green T-shirts showed up two years ago at the Federal Reserve’s annual conference in Jackson Hole, Wyo., they were regarded by many participants as an amusing addition.

Two years later, they have won a place on the schedule.

The protesters, who want the Fed to extend its economic stimulus campaign, are scheduled to meet on Thursday with eight members of the central bank’s policy-making committee. At the start of a conference devoted to esoteric debates about monetary policy, officials will hear from people struggling to make ends meet.

The Fed’s effort to show that it is listening to its critics reflects the central bank’s broader struggle to find its footing in an era whose great challenge is not the strength of inflation, but the weakness of economic growth.

Officials are wrestling with the limits of monetary policy, the focus of the conference, even as they try to address simmering discontent among liberals who want stronger action and among conservatives who say the Fed has done too much.

The meeting also represents an unlikely victory for Ady Barkan, the 32-year-old lawyer who decided in 2012 that liberals should pay more attention to monetary policy. He now heads the “Fed Up” campaign, a national coalition of community and labor groups that plans to bring more than 100 protesters to Jackson Hole.

“We want to make sure that regular voices are being heard,” Mr. Barkan said in beginning the campaign two years ago. The American economy, he said, was not working for all Americans — particularly not for blacks and other minority groups.

Fed officials so far have chosen to accommodate the group by applauding its efforts at public education, not by seriously engaging its arguments that interest rates should be raised more slowly. Esther George, the president of the Federal Reserve Bank of Kansas City, which hosts the Jackson Hole conference, arranged Thursday’s meeting with the activists. She said in an interview earlier this year that the Fed must balance job growth with other issues, like financial stability.

“I am completely sympathetic,” she said of the group’s concerns.

But she cautioned that the Fed’s powers were limited. Pushing too hard to lower unemployment could lead to higher inflation, or speculative bubbles, that would force the Fed to raise interest rates more quickly. The resulting economic volatility could end up doing more harm than good.

“The Federal Reserve has become somehow the answer to many problems far beyond what we can actually address,” she said. “I wish I could fix all of it with a tool like monetary policy. But we can’t.”

Even Mr. Barkan’s supporters acknowledge the long odds. Fed Up’s budget has grown to $2 million this year, from $145,000 in 2014, mostly from Good Ventures, a nonprofit foundation created by the Facebook co-founder Dustin Moskovitz, which describes the campaign as “relatively unlikely to have an impact.”

Fed Up’s more visible success has come in pursuit of a longer-term goal: advocating for changes in the Fed’s governance that could eventually shift its decision-making.

In a report published earlier this year, Fed Up highlighted the Fed’s lack of diversity. There are no blacks or Hispanics among the 17 officials on the Fed’s policy-making committee of 12 regional bank presidents and five governors. No black or Hispanic has ever served as president of a regional reserve bank.

Moreover, the report said that whites composed 83 percent of the directors of the Fed’s 12 regional reserve banks, who select the regional presidents.

Narayana Kocherlakota, former president of the Federal Reserve Bank of Minneapolis, said that the absence of minorities was “quite troubling.”

“Those kinds of persistent absences of key demographic groups really suggest that the appointment process, there is something that can be fixed there,” he said.

Fed Up also argued that bank executives should not sit on regional Fed boards. Under current law, bankers hold three of the nine seats on each board. The regional reserve banks are owned by the commercial banks in each district, although they operate under the authority of the Fed’s board, a government agency whose members are nominated by the president and confirmed by the Senate.

In May, 127 congressional Democrats signed a letter to Janet L. Yellen, the Fed chairwoman, calling attention to the Fed’s lack of diversity and the influence of the banking industry.

On the same day, a spokesman for Hillary Clinton’s presidential campaign said in a statement that “Secretary Clinton believes that the Fed needs to be more representative of America as a whole and that common sense reforms — like getting bankers off the boards of regional Federal Reserve Banks — are long overdue.”

Two months later, the Democratic Party adopted a campaign platform that included similar language, the first time in recent decades it mentioned the Fed.

Andrew Levin, an economist at Dartmouth College, said Fed Up’s greatest chance for significant influence was not in framing the current debate about interest rates, but in changing the Fed itself. He co-wrote a report that the campaign published Monday detailing a proposal to make the Fed a fully public institution.

“Having a diverse set of policy makers — including African-Americans and Hispanics — will influence the Fed’s decision-making,” he said. “And it should. The public should have confidence that the public is well represented at the F.O.M.C. table.”

Mr. Barkan started the “Fed Up” campaign after joining the Center for Popular Democracy in 2012, a few years after graduating from Yale Law School. He had read a 2011 article by the journalist Matthew Yglesias, titled “Fed Up.” Unions and other advocacy groups were focused on minimum-wage laws. Mr. Barkan was compelled by the argument that they also should be focused on interest rates.

“Even if they move once less over the course of several years, that’s still massive,” he said earlier this year. “The number of people who have jobs because of that, or higher wages, that dwarves a $15-an-hour wage increase in a smaller city.”

The campaign has gained traction in part because the Fed is eager to show that it is listening. During the first protest two years ago, Mr. Barkan approached Ms. Yellen, who listened politely and invited him to bring a group of workers to Washington, where she met with them in November 2014.

Lael Brainard, a Fed governor who plans to attend the Thursday meeting, made a point last year of visiting the parallel conference Mr. Barkan staged on the sidelines of the Fed event. And Mr. Barkan’s group has now succeeded in persuading each of the regional reserve presidents to meet with groups of local workers.

Neel Kashkari, the new president of the Federal Reserve Bank of Minneapolis, met with Fed Up’s local affiliate, Neighborhoods Organizing for Change, this month, telling the group that he shared their concern about the persistence of higher rates of unemployment among blacks and other minority groups.

Mr. Kashkari also accepted an invitation to spend a day with one of the group’s members, Rosheeda Credit, a Minneapolis resident who described the struggles she and her boyfriend faced to cover the cost of rent and child care for their five children.

“Walking a day in somebody else’s shoes is actually — it makes the anecdotes that much more real,” Mr. Kashkari, who arrived at the bank in January, told reporters after the meeting. “It influences how I think about the problems we face.”

By BINYAMIN APPELBAUM

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