And while Mr. DeSantis enjoys broad support among Republicans, soaring to re-election victory just six months ago, the latest primary polls show Mr. Trump gaining a sizable lead. The demeaning nicknames for Mr. DeSantis have spread widely on conservative social media, growing this year as Mr. Trump’s attacks increased. Mike Lindell, the MyPillow executive and an election denier, quickly found a role for Mr. DeSantis in his elaborate election fraud narrative. “Ron DeSantis is a Trojan horse,” Mr. Lindell said in a recent interview with The New York Times. Mr. DeSantis had once endorsed Covid-19 vaccines and celebrated as Floridians were rapidly vaccinated.