Each bill for an act passed by the General Assembly, but not engrossed prior to the final adjournment thereof, shall be engrossed, signed and presented to the Governor in the same manner as during the session of the General Assembly, such presentation to be not later than the twenty-fifth calendar day after its passage by the General Assembly. The Governor shall, within fifteen days from its receipt by him, either sign the same, endorsing his approval thereon, and transmit it to the Secretary of the State or transmit the same without his signature to said secretary. If any such unsigned bill is accompanied by a statement of the Governor’s objections thereto, it shall not become a law unless such bill is reconsidered and repassed by the General Assembly by at least a two-thirds vote of the members of each house of the General Assembly at the time of its reconvening; if not accompanied by such a statement, it shall, at the expiration of the constitutional limit of fifteen days after receipt by the Governor, become a law.