Let's not forget about the 3DS, though. This console actually has pretty decent third party support in spite of the massive dominance of smartphones. Most of these are Japanese devs, but I think the 3DS shows Nintendo a roadmap that they should follow to win back 3rd parties for the NX. The low-hanging fruit that they need to win over first are companies like Capcom and Square Enix as there is already a good relationship there.
Getting console staples like FIFA, Madden and Minecraft also shouldn't be too difficult since they are on just about every platform under the sun. It's going to be a lot tougher for Nintendo to win over devs like Naughty Dog and Bungie because I don't think that there is an existing relationship there, but if the NX picks up momentum then it is absolutely possible.
Regardless, though, Nintendo needs to be proactive about getting back 3rd party support. In all likelihood, the NX won't be as dominant as the SNES or 3DS where Nintendo could just sit back and wait for 3rd parties to come. They are going to have to go out and secure this support the same way that Sony and Microsoft does. It won't make the NX successful on its own but securing 3rd parties is one piece of the puzzle and Nintendo needs the NX to be firing on all cylinders.