Whenever a vacancy shall occur or exist in the office of Representative in Congress from this State during a session of Congress, or whenever such vacancy shall occur or exist at a time when the members of Congress shall be required to meet at any time previous to the next general election, the Governor shall issue, within ten days after the happening of said vacancy, or after the calling of an extraordinary session of Congress during the existence of said vacancy, a writ of election to the proper county board or boards of election and to the Secretary of the Commonwealth, for a special election to fill said vacancy, which election shall be held on a date named in said writ, which shall not be less than sixty (60) days after the issuance of said writ. In all other cases no such special election to fill said vacancy shall be held. The Governor may fix, in such writ of election, the date of the next ensuing primary or municipal election as the date for holding any such special election.