Nintendo says that 2 million Switches will initially ship. This means around 600,000 for the United States.
The Wii also had the first initial shipment be 2 million.
The Wii U shipped more at first (and Nintendo got burned which is why they are scaling back).
What is interesting here is that Nintendo got smart and is doing the launch in March. It never made sense to do a launch in November since the initial shipment would sell out anyway. It is essentially wasting a holiday’s sales on pre-orders.
Switch is going to be supply restrained until the 2017 holidays. Nintendo is making them as they did the Wii initially.