There is absolutely no reasonable chance that this system will ever be profitable and the Xbox One will most certainly sell several consoles for every Wii U system that is sold.
Nintendo has no incentive to push this generation any longer than need be since it's a lost cause with their only goal being to minimize the losses and hopefully change their momentum somehow so they can regain profitability with their next generation hardware. They're not even anywhere close to GameCube style sales performance here as they close in on the Wii U's two year anniversary (A system that was never sold at a loss, I might add).
They will let it stay around just long enough to provide some semblance of a reasonable lifespan to placate their dedicated fans. Fall 2016 which I'm betting on will mark the 4 year anniversary which is reasonably close to the 5 year or so average folks expect from Nintendo systems. Once that happens, they will quickly phase it out once their next generation hardware is ready to go just like Microsoft did with the Xbox.
And with all this hybrid handheld/console talk, the age of the 3DS, and the downward momentum of the system and its greatly diminished software calendar, it might happen even earlier with a Fall 2015 or spring 2016 date at the latest since the 3DS will be ripe by then. If a hybrid platform of some sort is indeed the course they're taking, it's going to be the timing for the need of a 3DS replacement that they're going to key off for deciding when to launch their next generation platform rather than keeping the failed Wii U going a while longer just to keep up appearances.