Cornell Belcher, a former Obama pollster, argues that Obama’s presidency, combined with the recent rash of tragic race-related incidents, has permanently transformed the electorate. “I reject this notion that we’re going to see a wholesale decline in black turnout now that Obama’s no longer running,” he told me. Belcher cited the African-American turnout figures during the 2014 midterm elections in Southern states like North Carolina, Georgia and Louisiana, which represented a higher share of the overall electorate than in 2010. Still, Belcher agreed with Thornell’s cautionary note, saying, “You’ve got to give them something to vote for.”

That view was echoed by Rodell Mollineau, who worked for years with Senator Harry Reid and is now a political consultant. “The activists at Netroots Nation were saying what many in the black community already think and feel, just more loudly,” Mollineau told me. “And you saw how, within minutes of that unplanned event, it totally dominated social media. If you’re a candidate and you’re tone-deaf to these dynamics, you’re going to face electoral problems.”

The African-American Republicans with whom I spoke saw an opportunity for G.O.P. candidates to cut into the black vote now that Obama is no longer on the ticket. “We think the African-American vote will be key in this election,” said Elroy Sailor, an adviser to Rand Paul. “The African-American community hasn’t been this politically engaged since the ’60s. President Obama did a really good job of energizing and mobilizing African-Americans. In this election cycle, however, we predict the Democrat nominee will not be able to take the African-American vote for granted.”

Paul — who has frequently visited black colleges and spoken out against discriminatory patterns in policing and sentencing — may have been particularly committed to peeling away some of the core Democratic electorate, but other Republicans are clearly reading the same voting totals. Former Gov. Rick Perry of Texas — a Tea Party favorite but also a staunch advocate for reducing nonviolent prison sentences — gave perhaps the most surprising speech of the campaign last month at the National Press Club, in which he acknowledged the important role of the federal government in enforcing civil rights.

In his candidacy-announcement speech last month, Gov. John Kasich of Ohio said: “You think about the troubles that many of our African-Americans still face today in the world where we have worked to provide equal rights and opportunities. Sometimes they’re not so sure. And I don’t blame them.” The political consultant and former Kasich legislative aide Ron Christie told me: “So many Republicans over the years have said, ‘Oh, you’re African-American, so let’s talk about crime or food stamps.’ Governor Kasich never pandered that way, which is why he got 26 percent of the black vote when he was re-elected in 2014.”

Doug Thornell is doubtful such overtures will bear any fruit for the G.O.P. “You look at how most of the Republican candidates have been in a rush to condemn Donald Trump for his recent comments,” he told me. “You didn’t hear that fire when he demanded that President Obama show his birth certificate. And I can tell you, that was deeply upsetting to a lot of African-Americans. Republicans had to deal with that baggage in 2012, and I think they also will in 2016.”

Nonetheless, Thornell agrees with Walter and Wasserman that Hillary Clinton is unlikely to inspire black turnout at the history-making levels achieved by Obama. I reached out to the Clinton senior spokeswoman Karen Finney (who is African-American) about the matter. Finney acknowledged that the black vote would be critical to her boss’s victory and pointed to the early attention Clinton has paid to issues important to African-Americans — as in the candidate’s first policy speech, on criminal-justice reform, at Columbia University this past April — as evidence that the campaign was taking the matter seriously. She also insisted that emphasizing such issues would not cost Clinton the working-class white voters who greatly favored her over Obama during the 2008 primaries.