Before it was called "The New Spirituality" it was called "the New Age Movement" as coined by Alice Bailey of the Theosophical Society; but before then, it was simply called the occult and mysticism.
We see mystical/occult meditative practices (contemplative prayer) being promoted heavily by many proponents of the Emerging Church. There are other ties being formed between the New Age movement and the Emergent Church movement, such as the 'dialogue' between Brian McLaren and leaders of the NAM: Dialoguing Among the Devil's Disciples?; Leonard Sweet likewise refers to many New Age Leaders as "Leaders of Light" and Ken Blanchard who is heading the Lead Like Jesus conferences as a colleague and fellow of Rick Warren routinely promoting and endorsing New Age books and authors. McLaren, Sweet and Blanchard are all Emergent in their perspective and practice.
For more on the duplicity of Postmodern mysticism and so-called Christianity see Satan, the First Postmodernist by Sandy Simpson from Deception in the Church ministries.