I'm quite glad that I ran across Cardinal Dulles' article on the Filioque. It has a very interesting section about the scriptural basis of that phrase in the creeed. The full text of the article can be found here.
In appraising the importance of the filioque, one must compare it with two other positions regarding the origin of the Spirit. The first, the so-called "monopatrist" position, affirms the procession of the Spirit from the Father alone. This was the formula preferred by Photius and his strict disciples, although it has little basis in the earlier Eastern tradition. The other Eastern formula, that the Spirit proceeds from the Father through the Son, is found in many Eastern fathers, including Epiphanius, Ephrem, Cyril of Alexandria, and John Damascene." This formula was also employed by the Patriarch Tarasius at the Second Council of Nicea (A.D. 787).11
The first Eastern alternative, "from the Father alone," if asserted in a rigid and exclusive way, has many disadvantages in comparison with thefilioque. It may be asked, most fundamentally, whether the monopatrist position can account for the terminology of the New Testament regarding the Holy Spirit. Admittedly we do not have any New Testament text which teaches formally that the Spirit proceeds from the Son, but a number of texts, read in convergence, seem to imply this. John 5:19, for example, says that the Son does only what He sees the Father doing-a statement which seems to refer to the externally existing Son and hence to imply that the Son, together with the Father, breathes forth the Spirit. In John 16:14 Jesus says that the Spirit of Truth will take from the Son what is the Son's and declare it to the believing community. This "taking" is often understood as referring to the procession. Then again, in the Revelation to John, the river of the water of life is said to flow from the throne of God and of the Lamb (Revelation 22:l). Read in conjunction with Ezekiel 36:25-26, John 3:5, John 4:10, and 1 John 5:6-8, this river of living water may be understood as the life-giving Spirit.
What is merely suggested by these texts is impressively confirmed by the titles given to the Spirit in the New Testament. He is repeatedly called the Spirit of the Son (Galatians 4:6), the Spirit of Jesus (Acts 16:7), the Spirit of the Lord (2 Corinthians 3:17), the Spirit of Christ (1 Peter 1:11), and the 'Spirit of Jesus Christ (Philippians 1: 19). It is not enough to declare that the Son sends the Spirit, as most monopatrists do, since it must be explained how the Son gets the power to send the Spirit as His own. Correctly insisting that the temporal truth must have an eternal ground, Karl Barth holds that the Spirit of the Son eternally proceeds from the Son.12