Chief Executive. The second key role of the governor is that of chief executive, Most state constitutions contain language indicating that the governor must take care that the laws are “faithfully executed,” perhaps the most obvious of the governor’s jobs.he power to reorganize the bureaucracy, a power possessed by governors in half of the states, is most useful in terms of the chief executive role. This power allows governors to organize the people and offices of the executive branch in such a way that the bureaucracy is more responsive to political control.