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At a New Orleans Hilton along the banks of the Mississippi River this month, rice farmers met to discuss agricultural futures. High school football players roamed the lobby.

On the third floor, the topics turned toward leftist political theory, with people debating ways to tax the rich and holding sessions with names like Socialists and “the Establishment” and Transitioning to Governing Power: Learning From Latin America.

This was a convention for the Democratic Socialists of America, a left-wing political group that is savoring a year of victories, such as Zohran Mamdani’s for mayor of New York City, and plotting its way to more.

For much of its 43-year history, the D.S.A.’s role in American politics was obscure, at best. But since Senator Bernie Sanders’s run for the White House in 2016, the group says, it has grown to more than 90,000 members. The D.S.A. also says it now has 250 Democratic Socialists in elected office across 40 states, a vast majority elected since 2018. Representative Alexandria Ocasio-Cortez is a member of New York City’s D.S.A. chapter. Mr. Sanders is a democratic socialist — lowercase d and s — but not a D.S.A. member. Many D.S.A. elected officials, like Mr. Mamdani, are members of the Democratic Party.

Compared with the country’s two major political parties, the D.S.A. remains tiny. But as income inequality soars, the group is attracting intense interest, and Mr. Mamdani’s victory in New York showed that for a candidate to be a Democratic Socialist is no longer disqualifying for many voters.

The D.S.A.’s vision for America is a multiracial democracy with an economy that benefits working-class and middle-income people. Members’ views are varied, but fundamentally they believe that American capitalism has been captured by corporate interests. They argue that markets should be strongly regulated or even controlled by democratic governments. Though the modern group was formed in 1982, the organization has roots in the United States dating to the late 19th century and the early socialist leader Eugene Debs.

Some of its policies, even if pursued, may not work. And many in the country’s establishment disagree with its views or consider it zealous. But the D.S.A.’s influence is growing anyway. For some Americans tired of living paycheck to paycheck and determined to stop the rise of the antidemocratic right, that radicalism is exactly the group’s appeal.

Now that Democratic Socialists are getting elected to office and winning power, the pressure is on. In New York City, Mr. Mamdani’s mayoralty will be seen as a test of whether socialists can govern. The D.S.A. is fiercely nonhierarchical, with a labyrinthine structure that tends to lend itself to infighting. But the conference in New Orleans by the group’s advocacy arm, the D.S.A. Fund, was highly organized. There were workshops on zoning reform, seminars on the dangers of Big Tech and sessions on the transition from activism to governing.