From a teacher's perspective, I would not like to put my time aside just in case there's a last-minute booking. I want to use my time productively, and I think it's appropriate to have a limit to how late a student can book a lesson.
Aside from Phil's suggestion for instant tutoring, if you want a specific teacher for tomorrow, then just write to that person and ask nicely. It's quite possible the teacher can fit you in. As far as putting it through the italki system, you could book a "dummy session", ie. a later session, after you agree on an earlier time.