“Women of color, particularly black women are the strongest part of the Democratic Party, the most loyal,” she said. “We need a ticket that reflects the diversity of America.”

There is no precedent for the selection of a black running mate. There is also little evidence that vice-presidential selections sway general elections in any meaningful way, including Mrs. Clinton’s selection of Mr. Kaine in 2016. Still, citing the dip in black turnout four years ago, and the importance of black urban centers such as Milwaukee, Philadelphia, Detroit, and Cleveland in the Electoral College, proponents like Mr. Sharpton argue that a black woman could help Mr. Biden.

In 2016, the black voter turnout rate in a presidential election declined for the first time in 20 years, it was seven percentage points lower than the record highs of Mr. Obama’s 2012 re-election. The black share of the electorate also slipped from 13 percent in 2012 to 12 percent in 2016, a difference of 1.5 million black voters, according to Ted Johnson, a senior fellow at the Brennan Center for Justice who studies how race affects voting behavior.

Aimee Allison, the founder of She The People, a political group aiming to increase participation from all women of color by three to five percentage points in the general election, said a survey of her organization’s members preferred Ms. Abrams, with Ms. Harris coming in second.

“Among black women primary voters, we saw Joe Biden was head and shoulders the pick,” Ms. Allison said. “But what we need to do now is expand across demographics to places where someone like Sanders showed strength — among Latinas in Texas and Nevada, and with Asian-Americans.”

But a preference for Ms. Abrams — or Ms. Harris — is far from a consensus opinion, with the jockeying wrapped up in part in personal histories and Washington power plays.

Speaker Nancy Pelosi has encouraged allies to float names of House members like Representatives Val Demings of Florida and Marcia Fudge of Ohio, according to people familiar with those conversations, in part to reward members of her caucus with a higher profile. Several leaders in the Congressional Black Caucus, an organization steeped in tradition, have preferred Ms. Harris, who is a member. Georgia politicians like Atlanta’s former mayor Kasim Reed and its current mayor, Keisha Lance Bottoms, who endorsed Mr. Biden early and is a top surrogate, are former political rivals of Ms. Abrams.