questionswhat is the cut-off purchase date to have your…

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It really depends on the item, and since you didn't specify I'm going to give you a general answer which is likely terrible and I apologize in advance.

If you are ordering a shirt, you really should pick overnight shipping by now.
If it is not a shirt AND it has a tag on the picture that it will arrive by Christmas, order away with confidence!
If it is not a shirt AND there is no arrives by Christmas tag on the product picture it may or may not get there in time.

Vague as that sounds, I'm hoping it helps you a little bit.