Because our car is already prepped and we've done the inspection of the car, all that's left is to a quick inspection to verify nothing changed and then execute the paperwork - likely 15 minutes. So as soon as Tesla is ready to give us the paperwork - we should be good-to-go, and will try to get it done this afternoon.
In Texas, paying for cars is more complicated because the Tesla Service Center can't actually sell us the car - we are buying a car from Tesla in California, and the local Service Center is only providing assistance in the delivery of the car. We can't pay them any money directly - so the payment has to be made electronically to Tesla via their website, because we can take possession of the car.
For my first car, when the nearest Service Center was in Denver, at the beginning of 2013, our car delivery was like buying any major product on Amazon. The order was placed on the internet, payment was made before the product was shipped, and UPS delivered to our front door (OK, it wasn't a big brown truck, UPS had subcontracted the transport to someone else). I'll admit there was considerable angst about giving Tesla over $100K for a car I hadn't even seen, and the delivery would be done without anyone from Tesla (and then the transport hit a deer in west Texas, ...). But everything worked out well that time...
With our S 100D, Tesla has made a lot of progress - and the local Service Center is making the delivery process much better. We're planning to make the electronic payment while we're at the Service Center, after we've completed our final inspection, and before we start executing the paperwork. As soon as the Tesla website confirms the EFT has been completed, they should be ready to give us the car.