I've been really busy lately and I've left a batch in primary for fifteen days. I will definitely have time to do it tomorrow, but I'm wondering if I should stay up late to do it tonight. At what point will it be ruined?
One more day won't make a difference. Most beers will be forgiving for up to 3 or more weeks in the primary. It mostly depends on the style and ferm temps.
i'm sure you'll be ok, like AXEGOD said, you can get away with letting it sit for 3-4 weeks. besides it'll give it a little extra time to clear out. no worries.