Yes, they can, but a minority of governors have already had laws passed preventing any mandates. Again, the minority, but people in those states travel all over, so a mandate in one may not help much if there is no mandate in the state next door. I personally think it should be a national mandate, since it is a public health crisis. Vaccine passports as well are fine with me. Start excluding the unvaccinated from lots of places, and some will eventually change their minds. Of course, that's after their lawsuits have been struck down in the courts.