For those you wonder how long it takes miles to post after you purchase something (for example I did a Groupon for 20% off +3emiles/dollar), here was the response.

"There is a 45 business day waiting period for the credit to be reflected in your account; as mentioned in the offer the 45 days begins after the close of the month in which the order was placed."

That means - it can be up to 3 months. Personally, it's not a big deal for me. However, if you are counting on the purchase to put you over the top in a short time frame, I'd plan accordingly.