From the podium, Rep. James Clyburn (D-S.C.), 83, took a call from the chief executive, who thanked South Carolinians for their support. Applause followed, with congratulations all around.

As the modest crowd dispersed, Mr. Clyburn spoke with the press. The veteran congressman and staunch Biden ally said that the president's support among black voters remained unshakable.

"The best illustration of that is that he got 96 percent of the vote in this primary," Mr. Clyburn said. "But his largest percentage—over 97 percent—was in the town of Orangeburg, where there are two HBCUs [historically black colleges and universities] and a community college."

"I go to an African American barbershop," Mr. Clyburn said. "I go to an African American Church. Joe Biden is as strong with African Americans as he has ever been."

Mr. Clyburn's view defies the findings of several recent polls and contradicts a trend that has been observable for several years. Namely, that Democrats have a problem with black voters, especially men. Hispanic voters, too.

Over the last eight years, minority voters have slowly but steadily migrated away from associating themselves with the Democratic Party, a movement that appears to be led by men.

An April poll from The Wall Street Journal shows that 30 percent of black men in battleground states intend to vote for Donald Trump. Hispanic voters who lean Republican are approaching parity with those who lean Democrat.

In simplest terms, analysts say, it amounts to a classic case of leaders being blind to generational change, taking their constituents for granted, and failing to deliver on the most basic function of government—to create conditions in which people can thrive.