For the entire primary, Mr. Kennedy led among the 24 candidates, a field noted mostly for the fact that it included David Duke, the former imperial wizard of the Ku Klux Klan, who came in a distant seventh. On Nov. 8, Donald J. Trump beat Hillary Clinton by a 20-point margin here, and Mr. Kennedy came in a comfortable first in the Senate primary with a quarter of the vote; Mr. Campbell’s second-place finish was more than seven points behind. Combining the votes of just the top three Republican candidates in the primary would reach a majority.

“Honestly it doesn’t look like Campbell has much of a path to victory,” said Gregory C. Rigamer, a pollster in New Orleans who has done analysis for a “super PAC” supporting Mr. Kennedy.

Still, Mr. Campbell does have one thing on his side: panicked urgency among Democrats nationwide.

“At this moment I don’t think it’s crazy to feel like our entire democratic institution is potentially under threat,” said David Skeist, 37, an actor in New York, who donated several hundred dollars to the Campbell campaign after reading about it on Facebook. Mr. Skeist knows that Mr. Campbell does not see eye to eye with him on some issues he considers important, like transgender rights or reproductive choice. But at the moment, Mr. Skeist is not alone in seeing full agreement as an unaffordable luxury.

The actress Rosie O’Donnell has highlighted the Campbell campaign on Twitter. The actor John Leguizamo urged people to donate, as did the comedian Patton Oswalt, who reposted an appeal for campaign donations with the words, “everyone please.”