It depends, in part, on how cold you keep your fridge. I keep at 33ยบ because I have a French Door with ice coming out of the top compartment. So, even thought there is a "mini-freezer" in my refrigerator compartment, if I don't keep it that cold, the ice re-freezes into a block and won't come through the chute. I find that I can keep stuff a fairly long time.
But, if you have any concerns, you should probably freeze and re-thaw a day ahead of time like GusRobin said.
BD