Except as provided in sections 4-5 to 4-8, inclusive, pertaining to department heads, including the State Board of Education, the Senate shall act finally upon each nomination or appointment made by the Governor and requiring the advice or consent of the Senate, within fifteen session days from the date on which such nomination or appointment has been communicated to it by the Governor, or before adjournment of the General Assembly sine die, whichever is sooner. If the Senate fails to act finally upon any such nomination or appointment within the time herein limited, the Governor may fill such office without Senate confirmation until the sixth Wednesday of the next session of the General Assembly and until a successor is elected or appointed and has qualified.