I think the Wii can make it.
People talk about Nintendo's new hardware replacing the Wii, but I'm not sure if that'll be the case. Even if Nintendo's new system is backwards compatible and successful, there may be use for a much cheaper, older system if they haven't experienced it yet.
Ask yourself this: how many years will it be into the next gen before Nintendo "replaces" games like Mario Kart Wii, New Super Mario Bros Wii, or Wii Sports Resort? These games will last years, seriously, unless replaced they'll still be selling in 2014 (+ more Wii games to come...)
The Wii's lifespan may depend on this question. I don't think the current Wii games will ever get old - the graphics are fine and all. It'd probably take Nintendo themselves killing the system off for it to die an early death. I guess if Nintendo's new console doesn't cost much more, is backwards compatible and uses new controllers (incompatible with Wii's) the Wii's hardware would drop quickly, but...