Nevertheless, to prohibit congregational singing of anything but the Old Testament psalms is an unwarranted addition to the word of God (cf. Deut.4:2) and -- ironically -- a violation of the regulative principle of worship thereby. The crucial question is this: Where in Scripture does God restrict His people to singing only the songs in the book of Psalms? No such restriction can be demonstrated. Those who try to infer it end up relying on fallacious arguments. Those who insist that we must positively demonstrate that anything we sing has the explicit warrant of Scripture have misunderstood and misapplied the "regulative principle" -- on a par with somebody who would hold that the very words of our prayers and sermons must have the explicit warrant of Scripture.
First, it is unreasonable to restrict singing to the 150 songs in the book of Psalms. These are not the only inspired songs in the Bible (e.g., the song of Moses, the magnificat of Mary, the psalms recorded outside the psalter). in Ezra 3:11 we read of the Levites singing words (after the time of the Psalter) which will not be found anywhere as such in the Psalms. David himself in the psalter said that God's people were to sing His "statues" and "all of His wondrous deeds." This takes us beyond the words of the Psalms!
Second, it is theologically deficient to restrict our praise to the old covenant anticipations of our Savior and His redemptive work. There is no question about the fact that Christ and His saving ministry are found in the words of the Psalms; praise the Lord for the Christology of that book! But it would be preposterous to think that the Christology and soteriology of the Psalms come anywhere close to the explicit, detailed, and clear teaching about Christ and salvation found after His incarnation and the actual accomplishment of redemption -- the Christology and soteriology of Paul, John, and the rest of the New Testament. We are New Covenant believers; although being one the the Old Testament people of God who enjoyed the same covenant of grace as we do, we enjoy a fuller revelation and better administration of the covenant than they did. Our worship and praise for God's deliverance should reflect that progress.
Third, it is erroneous to think of singing as a separate element of worship. Singing is rather just one of the many legitimate means of pursuing the various elements of worship. Prayer, praise, exhortation, and teaching are among the proper elements of worship (as regulated and restricted by the word of God). But all of these can be pursued by various means: meditation (e.g., silent prayer, reflection on Scripture), plain speech (e.g. praying aloud, preaching a sermon), OR in song (i.e., with increased melody and rhythm). Singing, you see, in just one of the ways in which we pray, or praise, or exhort, or teach one another.
Notice how Col.3:16 categorizes "psalms, hymns, and spiritual songs" as forms of teaching and admonition; this is one of the Biblically defined functions of song in worship (cf. I Chron. 25:1; I Chron 14:15, 26). Therefore, since it is not a separate element of worship, singing does not require a separate Biblical justification.
Fourth, it makes little sense to say that the words of our songs must come directly from the Bible (or psalms), when one does not likewise restrict the words of our sermons to what is directly found in the Bible! Both are forms of teaching and admonition. What reason could there be for holding that teaching-in-plain-voice may use words outside the Bible, but teaching-in-song may not use words outside the Bible? (E.g., I can say "A mighty fortress is our God" in a sermon, but we cannot add melody and sing the very same words!) Teaching is not identical with reading from Scripture (I Tim. 4:13) -- whether in song or not.
Finally, the exegesis of exclusive-psalm-singers is not acceptable at Colossians 3:16 and Ephesians 5:19. If these verses are referring to more than the songs of the book of Psalms, then it is acceptable for Christians to sing more than the songs from Psalms. Exclusive-psalm-singers must argue, then, that the words "psalms, hymns, and spiritual songs" in these verses all apply to the Psalms and can be applied to nothing but the Psalms. That is clearly mistaken, however. 2 Samuel 22 is not part of the book of Psalms, but it is called a "psalm" in verse 1; the new revelation of 1 Cor. 14:26 is obviously not from Psalms, but it is called a "psalm." Or take the word "hymn." Can this word (in itself) apply to compositions other than the those from the book of Psalms? Obviously, yes. Well then, is there anything about this word in the context of Col. 3 or Eph. 5 to restrict its referent to the book of Psalms? Not at all. Finally, exclusive-psalm-singers must argue that "spiritual song" must mean "inspired song" (thus being restricted to the words of Scripture for us). But the word "spiritual" does not mean the same thing as "inspired," as is clear from its use in 1 Cor. 2:15; 3:1; and Eph. 6:12. So then, "psalms, hymns, and spiritual songs" does indeed apply to the Psalms, but it is mistaken to argue that such words can apply only to the Psalms. (Likewise, the fact that "apostolic letters" can apply to the epistles of Paul does not prove that the expression applies only to Paul's letters!)
Therefore, I believe that the exclusive-psalm-singers do not rest the case for their position solely on Scripture. they cannot demonstrate that God prohibits singing anything but the Psalms in worship or that singing non-Psalms violates the regulative principle (any more than preaching words not recorded in Scripture). Their arguments are flawed by fallacious reasoning and exegetical mistakes. The persuasiveness of their position does not rest on Biblical authority, then, but rather on church tradition and subjective personal considerations (e.g., emotional attachment to the Psalms, which is quite understandable). It is not Reformed to allow such matters to control or restrict our worship.