A Nintendo patent from March 2006 shows that the company originally intended a Wii-mote style device for the GameCube. A patent drawing shows how the Wii Remote could link with the GC.
A Wavebird-like adapter would be attached to the GameCube console, which would interface with the wand remote. [[link]] There appears to be two separate sensors points on the television.
The wand remote in the patent drawings looks surprisingly similar to the finalized Wii-mote.
There is also a patent drawing for a tennis game — which includes a drawing of Mario. Early shades of Wii Tennis, no doubt. So [[link]] somewhere along the line, Nintendo decided to turn this add-on into the impetus for the console we now call the Wii.
[[link]]Update: Miyamoto has talked about the early incarnations of the Wii before. This newly released patent simply confirms earlier suspicions.
Nintendo Patent Reveals [Siliconera]