From the Postal Service, deadlines for shipping stuff to get there by Christmas
Domestic Mail Class/Product
Cut Off Date
First Class Mail
The sooner you get it done, the better though!
Save yourself some time (and some sanity) and print your priority mail postage online at usps.com and leave the package out for the carrier (it's cheaper if you print it online than if you pay at the post office too!)
Be sure to check out ups as well if you're sending a big or heavy package. It might be cheaper.