“Race is an underlying factor and dynamic among the Democrats in the Senate,” said Gerald Benjamin, a professor of political science at the State University of New York at New Paltz. “It’s always beneath the surface.”

The balance of power in the Senate is as confounding to insiders as outsiders. The Assembly and the executive branch, with Gov. Andrew M. Cuomo at the helm, are controlled by Democrats. But the Senate, historically led by Republicans, has the thinnest of margins. The 63-seat Senate now comprises 31 Republicans and 32 Democrats, including an empty seat that is likely to be filled by another Democrat this spring.

The eight breakaway Democrats who caucus with the Republicans are joined by Senator Simcha Felder of Brooklyn. A Democrat, he recently ran on the Republican line as well.

When Senator Jeffrey D. Klein, who represents parts of the Bronx and Westchester County, first broke from the mainstream Democrats to form the Independent Democratic Conference, there were four members, all of them white. It has since emerged as an independent faction in its own right. In recent months, the conference has grown more diverse as well; Ms. Alcantara successfully ran on the group’s line in the primary last year. Senator Jesse Hamilton of Brooklyn, who is black, joined the conference in the fall. And in January, Senator Jose R. Peralta of Queens, a first-generation Dominican-American, followed suit.

With President Trump’s victory prompting protests among liberal activists across the nation, renewed attention is being paid to the independent Democrats. Rallies and websites accuse them of betraying a liberal agenda by teaming with Republicans. That has put the Independent Democratic Conference on the defensive.