It's the latest fallout in the feud between DeSantis, a Republican widely seen as a potential 2024 presidential contender, and Disney, Florida's largest private employer, over a measure that bans schools from teaching young children about sexual orientation or gender identity.

After DeSantis signed the bill into law earlier Monday, the Walt Disney Company wrote in a statement that its "goal" was to get the law repealed or defeated in the courts.

DeSantis previously said Disney "crossed the line" with that statement. On Thursday, DeSantis went further, suggesting Disney's "special privileges" could be lifted.

"Disney has alienated a lot of people now," DeSantis said at a West Palm Beach press conference. "And so the political influence they're used to wielding, I think has dissipated. And so the question is, why would you want to have special privileges in the law at all? And I don't think that that we should."