This makes a great deal of sense. Jesus was painting Himself into a corner, relying on Israel’s prophetic tradition and demanding that He be judged in the same way that all prophets were judged---based on the verifiability of their predictions. In His actions in the Temple, Jesus presents Himself in the mold of Jeremiah, and does so by making reference to His very words. Had his words of the Creator God’s judgment against the Temple not come to pass, Jeremiah would have lambasted as a false prophet and held up to scorn rather than honor.
However, Jeremiah’s words did come to pass, the Temple fell, and even though His words were not exactly grand proclamations for Israel, he is held up as a great prophet of Israel (a prophet being one who calls corrupt powers to account, not necessarily one who makes predictions about the future). The same standard would have applied of Jesus. Would anybody listen to Him, or have any use for Him, if the singular distant prediction that He made, which was well understood to be a prediction about the demise of the Temple within the lifetimes of many of His hearers, did not occur? One would think that the answer to that question would be in the negative.
Certainly, the Resurrection was and is vital as a witness to Jesus. However, those that witnessed and interacted with the risen Jesus following His Resurrection were limited in number. Accordingly, skepticism towards such a claim would be natural and completely understandable, as people simply did not come back to life, especially after undergoing a Roman crucifixion. While Jesus obviously staked a great deal of validation on His Resurrection, He also appears to have staked a great deal on the fall of the Temple as well (and His biographers seem to have staked much on this claim as well).
If Jesus staked much on this claim, then His church could do no less. Not only did He claim that the Temple would fall, but perhaps more importantly, as it concerns the church that would follow Him, He claimed that when the Temple fell, He, as the Son of Man, would go (or have gone) before the Ancient of Days to receive His kingdom, power, and authority (or this event would be confirmation that this had in fact already occurred). Is this not important?
Now, to get a taste of where this idea might be headed, it could be said that one gets a sense of this way of thinking in the first chapter of Romans, as Paul declares that Jesus “was appointed Son-of-God-in-power according to the Holy Spirit by the Resurrection from the dead” (1:4a). The letter to the Romans, of course, was written between the Resurrection of Jesus and the fall of the Temple. If the early Christians knew that Jesus had staked His claim on the fall of the Temple, explicitly linking its fall with His receiving of His kingdom, then one can easily hear this as Paul speaking about this appointment as an appointment-in-waiting, expecting the validation to come. One can also imagine Him being quite confident that the validation would come, especially considering the fact that Jesus had risen from the dead and appeared to Paul, which was the basis for Paul’s dramatic transformation from persecutor of the church to its chief proponent and the originator of Christian theology/philosophy, and the complete re-orientation of his life around the claims of Jesus.
It is quite likely that, as the message of Jesus went forth, and as the church presented itself, through and in union with their risen Lord, as the new Temple, that Jesus’ words about the fall of the Temple that was to take place relatively soon had an important place in talk of Him. Why would this not be the case? Indeed, it would be odd if this was not the situation at hand. Why can such a thing be said? Well, one would have to consider the question in accordance with the fact that the issue of Jesus, as Messiah, was a primarily a Jewish issue.
Salvation for the world was to be through the Jews, and any proper understanding of the role of the Messiah cannot be divorced from the history of Israel and the Creator God’s role for His chosen people. Why would the Jews, especially, whose lives were oriented around the Temple, shift their allegiance from the Temple (and therefore the God represented by the Temple) to Jesus? It is a legitimate question. If they had the Temple, then why would they need to seek their God in some other place or person? It was the lack of the Temple, during the period of the Babylonian exile, that forced the Creator God’s people to seek Him.