One of the reasons candidates like Ms. Ocasio-Cortez and Ms. Salazar speak the language of class so fluently is that it’s central to their identities. Al Gore, John Kerry and Hillary Clinton struggled to cobble together a credible self out of the many selves they’d presented over the years, trying to find a personal story to fit the political moment. Today’s young candidates of the left tell a story of personal struggle that meshes with their political vision. Mr. Obama did that — but where his story reinforced a myth of national identity and inclusion, the socialists’ story is one of capitalism and exclusion: how, as millennials struggling with low wages and high rents and looming debt, they and their generation are denied the promise of freedom.

The stories of these candidates are socialist for another reason: They break with the nation-state. The geographic references of Ms. Ocasio-Cortez — or Ms. Tlaib, who is running to represent Michigan’s 13th District in Congress — are local rather than national, invoking the memory and outposts of American and European colonialism rather than the promise of the American dream.

Ms. Tlaib speaks of her Palestinian heritage and the cause of Palestine by way of the African-American struggle for civil rights in Detroit, while Ms. Ocasio-Cortez draws circuits of debt linking Puerto Rico, where her mother was born, and the Bronx, where she lives. Mr. Obama’s story also had its Hawaiian (as well as Indonesian and Kenyan) chapters. But where his ended on a note of incorporation, the cosmopolitan wanderer coming home to America, Ms. Tlaib and Ms. Ocasio-Cortez aren’t interested in that resolution. That refusal is also part of the socialist heritage.

Arguably the biggest boundary today’s socialists are willing to cross is the two-party system. In their campaigns, the message is clear: It’s not enough to criticize Donald Trump or the Republicans; the Democrats are also complicit in the rot of American life. And here the socialism of our moment meets up with the deepest currents of the American past.

Like the great transformative presidents, today’s socialist candidates reach beyond the parties to target a malignant social form: for Abraham Lincoln, it was the slavocracy; for Franklin Roosevelt, it was the economic royalists. The great realigners understood that any transformation of society requires a confrontation not just with the opposition but also with the political economy that underpins both parties. That’s why realigners so often opt for a language that neither party speaks. For Lincoln in the 1850s, confronting the Whigs and the Democrats, that language was free labor. For leftists in the 2010s, confronting the Republicans and the Democrats, it’s socialism.

To critics in the mainstream and further to the left, that language can seem slippery. With their talk of Medicare for All or increasing the minimum wage, these socialist candidates sound like New Deal or Great Society liberals. There’s not much discussion, yet, of classic socialist tenets like worker control or collective ownership of the means of production.