Nintendo doesn't even make the consoles. Foxconn (Hon Hai Precision) does. Foxconn actually assembles pretty much every must have gadget: PS2s, PS3s, 360s, iPods, iPhones, Wii, etc ...
In terms of degree of difficulty, for them it is pretty much a push.
What people have to realize is that production limitations for any console or device are usually due to the assembly partner, not the company whose name we associate with the appliance. Nintendo orders 1.8M Wii a month from Foxconn. They get these core units in assembled, then are tasked with flashing in the software, pairing a remote, a nunchuk, a power supply, a sensor bar, books, manuals, etc ... etc ... and getting the whole package boxed and ready to ship.
Whether it's Ninty, Sony, Microsoft, or anybody else, they can only box what they received from their assembly partners.
Increasing production mean ordering more GPUs from ATi, more CPUs from IBM, more MEMs sensors, more WiFi controllers, Bluetooth circuits, etc ... etc ... Upping capacity isn't as simple as "building a factory." Dozens of suppliers all have to be able to meet the demand, and all of these parts must arrive to Foxconn on time to assemble, then get back to Nintendo in concert with the paper products from the printers, yada yada yada. It becomes even more difficult when you consider that most of the core hardware in all our devices, like a WiFi or Bluetooth chip, is pretty much the same thing from the same source. Now that company is tasked with producing more chips for Wii, more for iPhones, more for 360s, and so on and so on.
The whole process isn't as simple as some people want to believe.








