Nintendo would probably be shunted to the handheld market. It's moving towards sort of a niche market as it is (party games + bizarre not-games like Wii Fit and some DS thing that's just a bunch of cooking recipes...). Take away the support for the Wii Fit, and I doubt they'd be able to rally in time for the next set of consoles. They might try to quickly put out some new, conventionalconsole after the Wii fails so badly, but it'd end up rushed and ultimately only the die hard fans would get it. Sort of like the Dreamcast, in a way.
The thing is, companies really can't recover from a horrible console crash, not the same way they can from a handheld. Consoles are sold at a loss, and rely on games sales to make up for it. With people not buying Wii games, and other Wiis lying in a warehouse, that's millions of unrecovered dollars going into manufacturing the consoles alone, let alone the complete lack of profit. Nintendo will just retreat back into the handheld market. You'll probably start seeing Mario on the XBox 720 or PS4, when they come out.
Edit: Also, I still think this is a slight possibility. Not a huge one, but I think we'll see Wii/accessory sales drop dramatically after XBox's Project Natal comes out. Natal basically does what the Wii does, but infinitely better. Full motion control, instead of just using a little Wiimote.