I don't believe a natural reading of this passage would lead someone to believe that Jesus was meaning this is something they would collectively acknowledge in some future setting before the 2nd coming.
But surely the “natural reading” for each of us follows our particular presuppositions. Preterist presuppositions yield the kind of “natural reading” you suggest, interpreting the “seeing” and “coming” as believing and receiving.
But to someone like Dr. Brown or myself, it seems inconceivable that it doesn’t mean more than that, because of the irony of the passage. For in the N.T. the phrase “cometh in the name of the Lord” occurs only in the gospels, and then only when either the people shouted it along with “Hosanna!” during the Triumphal Entry, or here, a day after the Triumphal Entry, when Jesus says (in Matthew 23:39, as well as in Luke 13:35) that they won’t see him again until they say, “Blessed is he who cometh in the name of the Lord.’ ” Imagine when the disciples heard Jesus say that. Wouldn’t they have thought: “But it was just
yesterday that Israel said those very words! Were you so sorrowful and weeping that you didn’t hear them? But surely you must have! But then, why do you discount those words?" The answer (we note) is that Israel that day uttered words without acknowledging their need of Him as their Savior, wanting only a political deliverer. That much would be evident in a few days, when they shouted a far different thing before Pilate.
And so, it seems natural to me that, in effect, Christ is saying, “You’re going to say the same thing again, but next time with understanding.”
What, then, is really the “natural reading”? Is it going to be one which, for Jarrod and Steve and for consistency’s sake, will of necessity have to be one in which you now further spiritualize the matter, so that the crowd’s use of the words “Blessed is He who cometh in the name of the Lord” pertains nothing to his actual physical descent into Jerusalem, but only to the spiritual blessings they may now expect to receive, having ‘seen’ Him, however fickle and temporary that would turn out to be?
I don’t find that kind of interpretation natural at all. It seems important here that we ought to recognize the similarity of wording between the crowd and Jesus’ echoing of it’s words.