What is the origin of the maha-mantra?
The maha-mantra is not something that originated or was "invented" at some point in history. It is recommended in the Brhan Naradia Purana (and many other Vedic texts) and is an incarnation of the Supreme Person Himself. He is the same as His name, and this maha-mantra was offered to the people in Kali-yuga as the Yuga-dharma (prime recommended method of spiritual realization) by Chaitanya Mahaprabhu who was Krishna Himself.
The Holy Name, in the form of the maha-mantra, makes the realization of God easy in this very difficult time, a time of quarrel and hypocrisy, a time where spiritual life is not "cool" and material "advancement" is all that matters. Chanting is easy, and puts us directly in touch with the Lord...because He appears there in the sincere chanting of His name.
“‘The holy name of Krishna is transcendentally blissful. It bestows all spiritual benedictions, for it is Krishna Himself, the reservoir of all pleasure. Krishna’s name is complete, and it is the form of all transcendental mellows. It is not a material name under any condition, and it is no less powerful than Krishna Himself. Since Krishna’s name is not contaminated by the material qualities, there is no question of its being involved with maya. Krishna’s name is always liberated and spiritual; it is never conditioned by the laws of material nature. This is because the name of Krishna and Krishna Himself are identical."
—Caitanya-Caritamrita, Madhya 17.133, quoted from the Padma Purana.