Ooooo, this is really neat! I just discovered a link between the logion being discussed and a statement by Paul:
Mark 14:58: "I will destroy (kataluein) this Temple (naon touton) that is made with hands, and in three days I will build (oikodomein) another, not made with hands (akheiropoiétos)".
John 2:19-20: "Destroy (lusate) this Temple (naon touton), and in three days I will raise it up...It has taken forty-six years to build (oikodométhé) this Temple, are you going to raise it up in three days?"
2 Corinthians 5:1: "If the earthly tent we live in is destroyed (kataluein), we have a building (oikodomé) from God, a house not made with hands (akheiropoiétos), eternal in the heavens".
Paul thus appears to be yet another witness to the saying, and the formal parallels are closer to Mark than John, but what is especially striking in Paul is that he shares the Johannine characterization of the "building" as referring to the body (earthly body = earthly tent, heavenly body = house not made with hands), and thus sides with John in this respect. The language is also applied to circumcision in Colossians, again supporting the somatic interpretation: "In him also you were circumcised with a circumcision made without hands (akheiropoiétos), by putting off the body of flesh in the circumcision of Christ" (2:11). All of this suggests that Temple=body interpretation in John is early as well.
However, the allusiveness of the saying itself in Mark 14:58 suggests a different original meaning of the logion. The phrase "not made with hands" (akheiropoiétos) derives from Daniel 2:34, 45, which describes a stone "not made with hands" (l' b-ydyn) that will "crush" (likmései, Th) the earlier kingdoms and establish an enduring kingdom (interpreted as the "Kingdom of God" in the gospels). The opposite phrase kheiropoiétos "made by hands" is also used in the OT (LXX) primarily to refer to idols (Leviticus 26:1, Isaiah 2:8, 10:11, 19:1), and most especially in Daniel (OG LXX) to refer to gods of gold and silver, "idols made by human hands (ta eidóla ta kheiropoiéta tón anthropón)" (cf. 5:4, 23, 6:28). Since the Temple is described as "made with hands" using this same word, there is a suggestion in light of the allusions to Daniel 2 and 5 that the Temple cult has idolatrous connotations and is destined to be overthrown when the Son of Man comes (cf. Mark 14:62, which is an allusion to Daniel 7:13-14). What is interesting about this view is how well it fits into the narrative setting of the saying in John....i.e. the cleansing of the Temple, sparked by outrage at the commercialism in the Temple (which put idolatrous images on coinage inside the Temple courts), and which according to v. 16 degraded the Temple into an unholy market. There is a similar interpretation of ch. 2 of Daniel in the Parable of the Wicked Tenants in Luke, which is viewed in the critical literature as another condemnation of the Temple cult (tenants = corrupt priesthood and Temple authorities), and v. 16 states that the owner of the vineyard "will come and destroy those tenants and give the vineyard to others"....a statement that evokes the saying about destroying the Temple and replacing it with a superior one. That Daniel 2 lurks behind the Lukan version of this parable can be seen in v. 17-18: "The very stone which the builders rejected has become the head of the corner. Everyone who falls on that stone will be broken to pieces, but when it falls on anyone it will crush (likmései) him". John seems to have preserved the appropriate setting for the more original apocalyptic understanding of the saying (i.e. closer to the apocalyptic source of the saying), but has interpreted the saying in terms of his overall realized eschatology, i.e. the saying was fulfilled in Christ's own death and resurrection.