Correct usage of a sentence with "is/was"? [closed]
Similar examples from Cambridge, though with different tenses, can explain the difference between the two situations:
I didn’t have any lunch today.
means that today is not finished but it is almost the end of the day and past lunchtime (there is no possibility to have lunch today).
I haven’t had any lunch today.
means it is still today and not too late to have lunch.
In both situations the time interval is today: it includes the moment of speech, but is not limited to it. The day is not finished.
Your option A could be re-written:
You haven't completed this task and your deadline is today. (it's your last chance to do it)
and Option B
You didn't complete this task today (and you missed the deadline).
In your sentence Today was your last day to complete this task, the past tense indicates that the speaker refers to a past interval/time included in what we call today, but prior to the moment of speech (an earlier moment today) with the intention to state that it is too late to change anything about the matter expressed in the sentence. Past tense is generally used to indicate
Definite time in the past (Cambridge)
The particularity of this sentence is simply that this past moment is included in the period called today and choosing either Option A or Option B to express it, will indicate if the matter discussed can still be subject to change or not.
Note that you can have similar situations with time phrases formed with the determiner this: this week, this month, this summer, this year, etc.
Consider:
This week was busy due to the promotion of our new app Sorted, and the preparation of AngelHack Hong Kong. (source) (the week approaches its end and the speaker looks back at the achievements that were accomplished earlier in the week).
and
This week is busy for many of us. Shopping, parties, holiday gatherings. It is a go, go, go week. (source) (the speaker has in mind the coming week, or the moment of speech is somewhere at the beginning of the week)