'First-time obedience' has had a foothold in Christian fundamentalism since the days of John Wesley's mother, who had fifteen children. She famously wrote, "Seldom is the odious noise of children crying to be heard in the house."
The concept was implemented in the Assembly from the beginning, based at first on James Dobson's books, then later on Fugate, the Ezzo's, and Michael and Debi Pearl. Ginger Geftakys advocates it even for infants in her pamphlet on child training.
Those who disagree with 'first-time obedience' focus on several issues: confusion between respect and fear, the primary goal of reaching the heart, developmental incapacity of young children, and neurological damage:
First Time Obedience?
First Time Obedience, Really?
Revisiting First Time Obedience
Does Discipline Really Produce Godly Character?