Florida Gov. Ron DeSantis has whipsawed his way through the national conversation this month, first by putting migrants on planes or buses to Democratic strongholds and then shifting to a more traditional role of crisis manager as one of the strongest hurricanes to ever hit the U.S. barreled into his state.

Facing a reelection in November that could be a precursor to a presidential campaign, the approach has been awkward at points. Navigating one of his state's darkest moments, DeSantis, a Republican, must partner with a Democratic president he has spent the better part of two years demeaning....