The GameCube had great games, decent (though not exceptional third party support), a good controller, was powerful, and quickly dropped to 100 dollars. That's incredibly cheap for a powerful console.
I think Nintendo's problem with home consoles isn't so much that they need to avoid making lots of mistakes, as they did with the N64 and the Wii U. I think their problem is that they fear that even if they do almost everything right -- as they did with the Gamecube -- they will still fail.
So yeah, price is definitely a factor. You could make an argument that the Wii is selling at a faster rate compared to the PS4 because it 150 dollars cheaper. The 3DS and the PS3 only took off when they received significant price cuts. But I think there are a whole slew of other problems that would hurt the Wii U even if it was a cheap system. The bigger problem for Nintendo, though, is the question of whether or not their next console will sell well even if they don't make tons of mistakes.
But if you want me to make a prediction, there would be no chance that a 100 dollar price cut would allow the Wii U to match the XB1.
