Where have I heard this before? I was just counting how many times the apostles call Mary the Mother of God and discuss her assumption and virginity and her being the mother of the church.
Of all the disagreements folks have with Catholic Marian practices and doctrine, I wish this was one we could put to rest. First, Elizabeth refers to Mary as 'the mother of My Lord.' I think we can all agree Mary was the mother of Our Lord. Also, I think we can all agree Our Lord is God. Hence, scripturally, there is a significant basis for arguing Mary is the Mother of God, since Mary is the mother of Our Lord and Our Lord is God.
Second, I know many of the posters who like to take potshots at the Marian title, Mother of God, are fully aware of the heretical movements the Church's adoption of this title was designed to combat -i.e. Nestorianism and Arianism. While you may not like the method, I would hope we are all in at least some agreement in our understanding of the Incarnation and the importance of stressing Jesus was both Man and God and that the adoption of this title was highlighted to drive that point home.