The deadline for changing is dependent on the fare rules, but so long as the ticket is changeable I would be surprised if the deadline is anything earlier than the check-in deadline for the flight for which you are currently booked.

Depending on what change you're trying to make, and which part of the ticket you're trying to change, and by how much, it is possible that delay will affect the amount you have to pay. For example, if the new fare is one that has an AP deadline that you'd satisfy tonight but you won't satisfy tomorrow, then making the change tomorrow could mean that you have to pay the difference to a higher fare. Or a booking class could sell out or be zeroed overnight. But we can only guess about things like this because we know so little about what you're trying to do.