It very likely is unconstitutional and would be struck down very quickly since there is existing precedence which ensure that Americans have the constitutional right to unabridged interstate travel.
So they want to target the Florida Governor, well what happens when California mutant variant numbers kick up? or NY? or Texas? It's an especially foolish strategy given what appears to be declining cases overall and increased numbers of vaccinations been administered.
What there're really are, are trial balloons being leaked to the press. It happens all the time when leaders can't make decisions. Last week was the domestic CV-19 testing requirement for all airline travel. It was met with swift resistance from virtually everyone impacted. This is more of the same, to gauge reaction. Remember these people don't care about the practical result of restrictions or the science, they care about the politics. And if they say that they will follow the "science" then you absolutely know that it is political.