The key to Nintendo getting third party support is having a powerful portable.
If they have a powerful portable, one that can even feasibly handle down-ports of PS4/XB1 games (960x540 res, lowered effects) ... they would get a lot of third party support because two problems would be solved with one stone ...
Third parties like the user base the DS and 3DS have, they are more skeptical about Nintendo's bipolar console fan base which has proven too up and down over the years. The problem with DS and 3DS though is they're too damn underpowered.
They can't run any type of modern game engine or anything that a publisher's developers have in the development pipeline so that means to make a DS or 3DS game a developer has to basically make an engine from scratch. And that's more trouble than its worth.
If Nintendo could change that ... it would be the holy grail of third party appeal for them anyway.
Now of course people will say this is impossible to have a portable that powerful and relatively affordable. I tend to disagree. The Apple A9X chip is reportedly specced at $38 to manufacture and that pumps out graphics that could probably open the door to PS4/XB1 ports on the portable.
Once you have developers making the portable version, then most of them will likely say "hell lets just make an enhanced console NX version too". Boom. Now you have third parties, that's how you sucker them in.