Do US state governors have jurisdiction over their airspace?
State governors do not have any control over their airspace but may have control over landing sites (read airports). From the FAA's brief on drone regulations:


  Congress has provided the FAA with exclusive authority to regulate
  aviation safety, the efficiency of the navigable airspace, and air
  traffic control, among other things. State and local governments are
  not permitted to regulate any type of aircraft operations, such as
  flight paths or altitudes, or the navigable airspace.
  
  However, these powers are not the same as regulation of aircraft
  landing sites, which involves local control of land and zoning. Laws
  traditionally related to state and local police power – including land
  use, zoning, privacy, and law enforcement operations – generally are
  not subject to federal regulation.