I've ordered rifles from the CMP quite a few times. I've gotten stuff usually in 4 weeks and as long as 6. The stuff I've ordered where in stock. The turn around time is also varies depending on the amount of orders they get and for what items.
That's why I stated 30-60 days since that's realistically what you should expect.
In recent orders, I would get an email after about a week of receipt stating that the order was received. Then 2 weeks later it would post in the estore. Then a week later it would ship. But I have 2 active orders right now, one for a bare receiver, and one for 2 rifles that are taking longer than that to process. It's all about patience.