The theology to which Fr. Carey referred was first articulated in the first chapter of the second part of Vatican II's Pastoral Constitution on the Church in the Modern World, Gaudium et Spes (par. 47-52).
The late Fr. Lawrence Boadt, a well-regarded Scripture scholar, stated what Fr. Carey only alluded to and did so succinctly and plainly in an article entitled "Scriptural Reflections on Marriage and Marital Love":
Since the Second Vatican Council, the Church's emphasis on marriage has been expressed much more in the spiritual categories of salvation, grace, and divine promise than in the language of legal contracts. By choosing the language of the Scriptures rather than canon law to redefine marriage, the Church avoids the appearance of stressing the need to merely hold on through the problems of married life and instead positively encourage couples to develop their relationship to Christ in order to turn difficulties into opportunities of loving concern and reject any indulgent self-love as the basis of their union. Through prayer, they may be assured that their marriage can survive and flourish, because it participates in the saving power of the covenant bond between God and Israel, Christ and the Church