Third party support on the follow-up to the Wii depends almost entirely on two things:
How high the quality of 3rd party software is on the 3DS.
and
If Nintendo fans actually start buying third party games.
If gamers and (Nintendo fans especially) buy a well-rounded variety of 3DS launch titles, it'll bode well for future 3rd party support. If all they do is spend their money on slighty improved N64 games we all played to death over the last 14 years, and ignore serious 3rd party efforts like Resident Evil, Street Fighter, MGS (which is also a port, but of a much more recent title), etc; then the sadly typical cycle of 3rd party companies abandoning the [Nintendo] system due to ignored software will happen once again.
Frankly, I wish it was launching with a Castlevania game. Castlevania was the first franchise on my last two Nintendo portable systems. Be fun to keep that going, like a tradition.