Tad Devine, a senior campaign adviser, said he understood that Mrs. Clinton had an advantage in the state. But, Mr. Devine added, the Sanders campaign has invested heavily in advertising targeting black voters in the state, with $711,000 spent on television and cable advertising and $381,000 on black radio stations.NYTBen Tulchin, a pollster for the Sanders campaign, said Mr. Sanders was focused on making sure he got to states with large black populations in the Midwest and in battleground states that would be crucial to winning the general election.

“South Carolina is a deep red state, but Bernie is doing better in battleground states with large African-American populations like Michigan, like Illinois, like Ohio, which have real bearing on this race and the primary but also have real bearing in the general election,” Mr. Tulchin said. “The reality is South Carolina is not a battleground state in the general election, right? So even if we can’t close it there, it has no bearing whatsoever in the general election, right?”