I'd call for the whole week. But then again, we detest moving once we've checked in. For us, it would be either move the entire reservation or none of it.
On the other hand, day by day gives you your best chance of getting it if all days are not available.
I guess you could call on the first day of day by day and see how it looks. If they say it looks like no problem, you can then just call at the end.