I can now confirm the existence of the Xbox Wiimote clone project and I can tell you the project code name : "Newton"
The "Newton" controller's code name is after the physicist Sir Isaac Newton. The internal Microsoft engineering code name is for this controller is "Newton" as in Newtonian Physics relating to gravity, inertia and acceleration. This is not to be confused with the defunct Apple Newton PDA, this is just and internal name, when this controller comes to market it will have a retail name.
The hardware is still being worked on and it might be a couple months before we see leaked shots of prototypes when they start to mass manufacture it but I am sure that there is an early software developer kit and prototype out there.
Nintendo is not the first company to make something like the Wiimote. The concept for the Wiimote has been called a 3d Mouse or a "Flying Mouse". There is a company called Gyration that makes wireless controllers and is an early innovator in these kind of controllers. Gyration owns a lot of applicable patents for motion-sensing controllers and in 2001 Nintendo hired the company to help them design a motion sensing one handed controller that eventually became the Wiimote.
Nintendo is an investor in Gyration but they don't own it. In 2001 Nintendo licensed patents from Gyration and used it to develop the Wii. They are US application patents 5898421 and 5440326 which are about a device tracking human motion and translating it into linear movement of computer graphic images. So Nintendo does not wholly own all the patents involved in the Wiimote.
Take a look at the awesome infomercial for Gyration's wireless mouse.
Microsoft is rumored to have licensed patents from Gyration and are using them to develop their motion sensing Wiimote controller. Legally Microsoft is not ripping off Nintendo but rather licensing the technology from the same place that Nintendo got it. For an example the Guitar Hero and Rockband controllers both use the same patent that is owned by Konami that they developed for Guitar Freaks.
Back in January there was a notice for a job at Microsoft for a hardware test engineer that drops some big tips about the "Newton" project.