"Blessed are the Breasts" (Did Christ downplay His mother?)

St. Mary with Jesus, Elisabeth Sarani

Our Protestant brethren sometimes object to the Catholic/Orthodox veneration of Christ’s mother, Mary. They find it to be pious exaggeration or even blasphemous. Some even believe the Scriptures anticipated this phenomenon, and readily prescribed the proper attitude to rectify such behavior: they point to this passage in the Gospel of St. Luke:

While [Jesus] was saying this, a woman in the crowd raised her voice and said to him, “Blessed is the womb that bore you and the breasts that nursed you!” But he said, “Blessed rather are those who hear the word of God and obey it!”
Luke 11:27-28

Is Jesus really downplaying His Mother? Is this a fair textual deduction of the passage?

No. And here’s why:

It might be understandably read that way if read in isolation from the rest of Scripture’s testimony, but such an isolation would go against the obvious messages found in other places of Scripture. Mary is, in many places, affirmed outrightly to be blessed. What’s more, these passages are found in the same book of the Bible: the Gospel of Luke.

And [the angel Gabriel] came to her [Mary] and said, “Greetings, favored one! The Lord is with you.
(Like 1:28)

When Elizabeth heard Mary’s greeting, the child leaped in her womb. And Elizabeth was filled with the Holy Spirit and exclaimed with a loud cry, “Blessed are you among women, and blessed is the fruit of your womb..." 
(1:41-42)

"Surely, from now on all generations will call me blessed;"
(1:48b)

The angel Gabriel addressed her as "highly favored one." Her cousin Elizabeth, being full of the Holy Spirit, declares that she is “blessed among all women.” And finally, in her own hymn of praise, Mary states that all generations will call her “blessed.”

Is Jesus, the Second Person of the Trinity, contradicting the testimony of Third via St. Elizabeth? Of course not. There is no way around; Mary is unambiguously consideried to be blessed, by the angel Gabriel, by her relative Elizabeth, and in her own hymn of praise unto God. Christ's words should not therefore be taken to deny any such thing. It would be denying the explicit testimony of Scripture, creating textual dissonance, to read the Messiah’s words in such a way as to suggest that being his mother was not special.

Having established that the passage should be seen in no way to contradict that Mary is, in fact, blessed, let us now move forward to see what it is Christ does define as being truly blessed. He says "blessed rather are those who hear the word of God and keep it." Are the two notions utterly unrelated?

Having been instructed by the angel that she will be "the virgin [who] shall conceive and bear a son" (Isaiah 7:14), how does the Virgin Mary respond?

"Here am I, the servant of the Lord; let it be with me according to your word."
(Luke 1:38) 

Who can fail to see that this is exactly what "hearing the word of God and keeping it" looks like? Mary is rightly called blessed on account of her obedience to the message of God. Obedience is better than sacrifice. Mary's role in birthing the savior is blessed in itself, but what makes her especially blessed but her obedience. Jesus is in no way denying that his mother is blessed among women, but rather, He is indicating the true source of blessedness, including her own. It wasn't her motherhood which rendered her a worthy disciple; it was her discipleship which rendered her a worthy mother. In reference to this very same passage, St. Augustine of Hippo so aptly expresses the concept thus:

"Thus also her nearness as a Mother would have been of no profit to Mary, had she not borne Christ in her heart after a more blessed manner than in her flesh." (On Holy Virginity par. 5) 

Yet even in light of all this, it's still reasonable to hold that the office itself of being Christ's mother indeed contributes to her being blessed among all women. It isn't somehow arbitrary or unimportant. Evidence for this is, again, found in Luke's Gospel itself. Following her declaration that "blessed are you among women, and blessed is the fruit of your womb", Elizabeth also iterates...

And why has this happened to me, that the mother of my Lord comes to me? 
Luke 1:43

If we look at the text honestly, we will see that Elizabeth specifically expresses that the Blessed Virgin herself, being the mother of the Lord, as contributing to the happiness of the occasion.

So, ultimately, let us not do damage against the Lucan account of the Holy Gospel by seeing Christ's words as somehow denouncing his mother. There is no need to pit "blessed are you among women, and blessed is the fruit of your womb" against "blessed are those who hear the word of God and observe it!" The Lord, though revealing a deeper spiritual truth, is not at all denying the beatitude to such a woman as his mother. She is blessed among all women because she is His mother, and she is His mother because she the one par excellence who "hears the word of God and observes it." The Word of the Lord not only took root in her heart, but it also took root in her womb, and in so doing, "the Word became flesh and dwelt among us."