What is the biblical support for the Nicene creed's statement of the Son being "eternally begotten"? What is the biblical support for the Nicene Creed's statement of the Son being "eternally begotten"?
Lee Irons addresses this question in his paper, "The Eternal Generation of the Son."  In response to the question of exegetical basis for the doctrine, he writes:


  Traditionally, the doctrine of the eternal generation of the Son was supported by an appeal to the five Johannine texts in which Christ is identified as monogenes (Jn 1:14, 18; 3:16, 18; I Jn 4:9). As early as Jerome's Vulgate, this word was understood in the sense of "only begotten" (unigenitus), and the tradition was continued by the Authorized Version.


Irons admits that modern scholars often reject this understanding of monogenes, but he contends that the traditional understanding is preferable. Following a textual variant, he renders John 1:18 as follows:


  No one has ever seen God, but the only begotten God, who is in the Father's bosom, has made him known


Now we must ask, in what sense is Jesus begotten?  Our experience with "begottenness" is always temporal – a baby does not exist, and then it is begotten and comes into existence.  The fathers at Nicaea, responding to Arianism, wanted to defend the eternity of the Son, so they said "eternally begotten" in their creed.  Though perhaps Schaff's translation of the phrase is more accurate:


  begotten of the Father before all worlds


Such language is reminiscent of several biblical passages, like John 17:5:


  And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was.


And Colossians 1:15–17:


  Who is the image of the invisible God, the firstborn of every creature [...] 17 And he is before all things, and by him all things consist.


Irons concludes:


  The framers of the [Nicene] creed interpreted the Johannine monogenes in the traditional sense [...] The fathers of Nicea seem to have believed that the biblical teaching regarding the generation of the Son (as indicated by the term monogenes) was powerful evidence that he is homoousios with the Father!