I'm guessing that the girl having barely a day left before dying is probably because her implied clumsiness is destined to put her in a position where she gets accidentally killed by that time, whether from falling down a flight the stairs and breaking her neck or getting run over by a car. Kotobuki accepting her confession would logically imply that she would have some sort of effect on the girl's routine that averts that deadly event (could be as "simple" as the girl not being at that location entirely, or could be that Kotobuki in the right time and place to save the girl's life).
Furthermore, by the girl's line after the confession, I suspect that had she been rejected, she would've been driven into such a deep grief that she might have outright died from it within mere hours or even minutes (i.e. the clock would've abruptly run down by several hours in the span of seconds); as clumsy as she seems to be, it wouldn't be implausible that the rejection-induced despair would put her in such a daze that she'd quickly find herself absent-mindedly walking straight into the path of a speeding car and getting fatally hit.