If you Pay'n'Spray in a way that would push you over midnight, you start the day over. Why? No idea, but that's how the game works.
The date is available 3 hours before the scheduled time. It showed up, as you can see on the minimap, at 21:00. I assume it would stay until 03:05 on Sunday, after exploiting the pay n spray bug which put you back ~21 hours. It's possible that it may have stayed available until the clock reached 03:05 on Monday, an additional ~27 hours, but I'm not sure. I doubt this would ever be useful, regardless if it'd stay an extra ~27 hours or not.
I remember many years ago viewing the beginning of a highlighted run which started just as the previous attempt was coming to a semi-disastrous close. Sometimes a VOD like this was accompanied by a remark signaling frustration or lost hope which, I suppose, the runner felt was a bit of amusing juxta