Mine was more like 11 days from ordering to getting a request to confirm my order, and then one more day to set up an appointment to pick up the car as early as July 3rd (which I naturally selected). All pertinent details in my .sig. Being within 20 miles of Fremont certainly helped. I was initially surprised that the VIN was in the high 44,400s as I've seen others that are scheduled to pick up their cars around the same time, albeit on the other side of the country, having VINs barely, or not even in the 30,000s. Then I thought about the distinct possibility that Tesla has been stockpiling cars in various parts of the country waiting for today.
I believe that the 3-5 months is indeed a placeholder depending upon the final configuration of the car. If you select the standard "first build" configuration (RWD/PUP/LR) then your car is probably already sitting in the lot in Fremont. If, however, you are waiting for AWD, then that's probably going to be some time longer. The good news is that as long as Tesla has calculated their sales numbers correctly and have managed to deliver their 200,000th US car sometime today or afterwards, then full the Federal tax credit will in effect to the end of this year.