My first impression upon reading the Joint Federal Vision Statement was one of surprise that, of the 18 loci addressed, postmillennialism is listed so early in the document (second only to "The Triune God"). Not that I desire to commit the ordo docendi, ordo credendi fallacy (i.e., that the order in which something is taught determines the order of its importance), but I do find this interesting.
The argument of the Joint Statement, in a nutshell, is that (1) If Jesus is the Savior of "the world," (2) If "all nations" will come to him, and (3) If the content of the Abrahamic promise is that "all the nations of the world would be blessed, and that his descendants would be like the stars in number," that therefore "prior to the second coming of our Lord Jesus, the earth will be as full of the knowledge of the Lord as the waters cover the sea."
Concerning the final day, the last sentence of our Confession says that Jesus "will have that day unknown to men, that they may shake off all carnal security, and be always watchful, because they know not at what hour the Lord will come; and may be ever prepared to say, 'Come Lord Jesus, come quickly.' Amen."
It seems to me that the arguments put forward by the Federal Visionists to prove the Christianization of the world are similar to those used by Arminians to insist that Jesus atoned for the sins of every single person. The Calvinist response, of course, is that when the Scripture says that Christ died for "all men," it means that he died for all without distinction, not all without exception. The same response can be offered here.
So in addition to the fact that our Standards neither hint at, nor seem to make room for, a Christianization of the world before the (supposedly) imminent return of our Lord, the postmillennial position seems to rest upon a woodenly-literal hermeneutic.
Yes, "all nations" will come to Christ, but in accord with the Joint Statement's insistence upon Scripture interpreting Scripture, the twenty-four elders in Revelation explain this by saying that the Lamb "has redeemed men to God from every kindred, tongue, people, and nation."