The Rev. Joseph Darby, first vice president of the Charleston, South Carolina, branch of the NAACP, has narrowed his choice to three candidates in the Democratic presidential race.

“I like Biden, I like Warren, I like Harris. They are probably my top three,” he told The Washington Times.

What about Sen. Cory A. Booker of New Jersey who, with Sen. Kamala D. Harris of California, is one of the most prominent black candidates in the race?

“It’s hard to say. Actually, he ought to be on the list, but I’m more impressed with those three,” Mr. Darby said. “There’s nothing that’s turning me off. He is enthusiastic. I’ll give him that. But for whatever reason, his message isn’t resonating like those other three.”

Mr. Darby’s assessment cut to the heart of the turmoil at the Booker campaign: He ought to be on the list, but he’s not.

Mr. Booker’s presidential bid looks good on paper. He stands out as a youthful 50-year-old black politician with an inspirational message of racial justice and love.

He is a former mayor of hardscrabble Newark, New Jersey, who ascended to the U.S. Senate. If that’s not enough, he is dating Hollywood star Rosario Dawson.

Yet Mr. Booker remains mired in the low single digits in national and early voting state polls. He trails far behind with black voters, which has hobbled his campaign across the country but especially in South Carolina, home to the first primary in the South and the crucial early test of support from a crucial bloc within the Democratic Party.

Democratic Party strategist Brad Bannon said Ms. Harris simply beat Mr. Booker in the “battle of identity politics.”

“Black voters make up approximately a quarter of the Democratic primary electorate, and there was only room for one black presidential candidate — especially with Biden drawing black legacy votes,” he said.

He credited Ms. Harris with getting out of the starting gate faster than Mr. Booker and dominating media coverage during confirmation hearings for Supreme Court Justice Brett M. Kavanaugh.

“Math matters, too,” said Mr. Bannon, going on to point out another advantage Ms. Harris has over Mr. Booker. “About 60% of the Democratic voters are female.”

Mr. Booker recently turned up the voltage on his already supercharged delivery on the stump.

He has been trading jabs with former Vice President Joseph R. Biden, slamming the front-runner for his role in a 1994 crime bill that he blamed for mass incarcerations of black men.

The clash over racial justice — an issue on which Mr. Booker built his political brand — foreshadows a showdown this week when the two men share the stage in Detroit at the second 2020 Democratic debate.

Mr. Booker also has grabbed headlines with antics such as geeking out at Comic-Con in San Diego and forgoing hotels to crash on couches at the homes of supporters along the campaign trail.

His poll numbers, however, haven’t moved.

“The Biden skirmishes on race and criminal justice help him get press coverage, but not on his own terms. So is it worth it? Clearly, he’s just not connecting,” said Christy Setzer, a Democratic political analyst in Washington.

Several officials with the Booker campaign said they feel good about his position in the race.

Some noted that at this stage of the 2016 Republican primary contest, legacy candidate Jeb Bush was in the lead and Donald Trump had just descended the golden escalator.

Others compared Mr. Booker’s position in the race to that of Barack Obama in summer 2017, when the overwhelming front-runner was Hillary Clinton, also a high-profile figure from the previous Democratic administration like Mr. Biden is now.

“He is in a spot where, when his time comes, and I think it will, he’s got the ground game to take advantage of it,” said James Demers, an adviser to the Booker campaign in New Hampshire. “He is going to start to move up.”

Still, a South Carolina poll released Thursday underscored Mr. Booker’s problems. He finished sixth in the state with 2% of likely Democratic primary voters and 2% of black voters.

Tom Steyer, a hedge fund billionaire and Democratic Party activist who jumped into the race about two weeks ago, matched Mr. Booker’s 2% in the overall vote and with black voters, according to the Monmouth University poll released Thursday.

Mr. Booker has held 34 campaign events in South Carolina, tying Ms. Harris for the most events in the state among the Democratic hopefuls, according to a candidate tracker by The Post and Courier of Charleston. Mr. Steyer has hosted just five events in the Palmetto State.

In that South Carolina poll, Mr. Biden led with 39% overall and a whopping 51% of black voters.

“We do have plans to do something to turn that around,” said Rhonda Rawlings, a spokeswoman for the Booker campaign in South Carolina.

The campaign had been hosting watch parties across the state with a screening of the documentary “Street Fight.” The film chronicles the 2002 mayoral race in Newark in which Mr. Booker, then a City Council member, mounts a scrappy but ultimately unsuccessful primary challenge against longtime Democratic machine politician Sharpe James.

“We’ve had really positive feedback on that,” said Ms. Rawlings. “I think a lot of people are seeing the senator’s tenacity. He is a proven leader.”

Mr. Booker ran again in 2006 and won the mayor’s race after beating Deputy Mayor Ronald Rice in the Democratic primary. During two years as mayor, he significantly expanded affordable housing, recreation centers and charter schools, and he launched a prisoner re-entry program.

He is running on a message of love and unity and says the 2020 election is a “moral moment in America.”

Asked Thursday whether he would change his message to better appeal to Democrats looking for a fighter to take on President Trump, Mr. Booker said “absolutely not” and urged voters to watch the documentary.

“Anybody who knows me [and] my emergence in Newark, New Jersey, knows that you can’t win elections in Brick City without being tough and being a fighter,” he said at a forum at the National Urban League’s annual conference in Indianapolis.

“You can’t win in Newark unless you can take on bullies and beat them. You can’t win in Newark unless you can take on demagoguery,” he said. “My history is taking on tough fights.”

• David Sherfinski contributed to this report.

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