101. The Liturgy frequently celebrates the Blessed Virgin Mary in an exemplary way during the season of Advent(Cf. Paul VI, Marialis Cultus 4). It recalls the women of the Old Testament who prefigured and prophesied her mission; it exalts her faith and the humility with which she promptly and totally submitted to God’s plan of salvation; it highlights her presence in the events of grace preceding the birth of the Savior. Popular piety also devotes particular attention to the Blessed Virgin Mary during Advent, as is evident from the many pious exercised practised at this time, especially the novena of the Immaculate Conception and of Christmas.
However, the significance of Advent, “that time which is particularly apt for the cult of the Mother of God”(Cf. Paul VI, Apostolic Exhortation Marialis Cultus 4), is such that it cannot be represented merely as a “Marian month”.
I’m not familiar with any impulse to make December a “Marian month.” Mary is such a part of the liturgy and religious culture of the weeks before Christmas, it wouldn’t add anything.
We also have the witness of our Eastern sisters and brothers:
In the calendars of the Oriental Churches, the period of preparation for the celebration of the manifestation (Advent) of divine salvation (Theophany) in the mysteries of Christmas-Epiphany of the Only Son of God, is markedly Marian in character. Attention is concentrated on preparation for the Lord’s coming in the Deipara. For the Orientals, all Marian mysteries are Christological mysteries since they refer to the mystery of our salvation in Christ. In the Coptic rite, the Lauds of the Virgin Mary are sung in the Theotokia. Among the Syrians, Advent is referred to as the Subbara or Annunciation, so as to highlight its Marian character. The Byzantine Rite prepares for Christmas with a whole series of Marian feasts and rituals.
The Directory on Popular Piety and the Liturgy is online at the Vatican site.