-->
My interpolation of the words "on that Day" and the (linguistically permissible) attribution of futurity to the past-tense verb qala is based on the identical interpretation of the above phrase by great commentators like Abu Muslim (as quoted by Razi) or Baghawi.
I.e., as mere wishful thinking and, therefore, of no account, or as something that in the course of time has "ceased to be relevant". Since many of those whom the message of the Qur'an has reached did and do regard it as a divine revelation and therefore as most "relevant" in every sense of the word, it is obvious that the expression "my people" cannot possibly denote here all of the Prophet's community (either in the national or in the ideological sense of this word), but signifies only such of his nominal followers as have lost all real faith in the Qur'anic message: hence the necessity of interpolating the (elliptically implied) words "some of" before "my people".
"My people" are of course the unbelieving Quraish. They treated the Qur-an with neglect, i.e., something to be discarded. But they were only a handful of people whose vested interests were touched by the beneficent reforms initiated by Islam. They soon passed away, and all Arabic-speaking or Arabic-understanding people have considered the Qur-an as a treasury of Truths expressed in the most beautiful possible language, with a meaning that grows deeper with research.