Hi,
Much depends on the sentence/context that contains the expresssion. Here are a couple of comments.
1. Does "the day" mean that particular day, but we don't know what exact day it is? What do you mean? I know but I don't know?
eg I can't remember the day that I first met him.
eg I will never forget the day that I first met him.
2. Does "the day or two" mean that particular day and the following day or two?
eg The day or two after I first met him were wonderful. ( This really just means a period of a few days. It's a rather vague expression. )
Best wishes, Clive