“Let’s be honest; he was the vice president under the first African-American president so his early name recognition was really high and that lifted his numbers,” said John King, a state lawmaker who recently endorsed Mr. Steyer.

The heightened stakes have made other challenges more apparent, including the sometimes awkward fit between Mr. Biden and a new generation of young, black elected officials who are sweeping the South. Compared with Mr. Clyburn’s generation, this group is less moved by arguments of deference and the chummy collegiality of beltway politics. Instead, they view themselves as ambitious insurgents.

One of the up-and-comers, Mr. Moore, ticked off a list of what he views as blemishes on Mr. Biden’s record that should be barriers for black voters: Mr. Biden’s past support for crime bills that some experts argue resulted in harsh sentences for black offenders; his treatment of Anita Hill during Clarence Thomas’s Supreme Court confirmation hearing; and his eulogy for Strom Thurmond, the state’s onetime Dixiecrat senator.

“Joe Biden wasn’t selected as a running mate for Barack Obama because he was a civil rights activist,” said Mr. Moore, who had supported Senator Kamala Harris before she withdrew. “It was because he was a safe white choice.”

Mr. Biden has caused some of his own problems. During a private meeting with prominent black mayors in Georgia last year, according to three people with direct knowledge of the gathering, he caused a stir when answering a question about education reform. Mr. Biden said one problem black communities face is that the “parents can’t read or write themselves,” a remark that shocked and frustrated many in the close-knit group.

In a statement, Mr. Biden’s campaign said he was seeking to reference his own experience.

“The Vice President regularly talks about how his father’s experience has shaped the way he feels about and views the relationship between parents and their children’s learning,” the statement said.

As he works to shore up his support here, Mr. Biden must rely on components of his campaign that were never the strongest. Mr. Biden’s fund-raising organization, for instance, was never robust in South Carolina and throughout areas of the South with heavy black populations.