Can Nintendo's lightning strike thrice?

Successful exploitation of novel control systems: the touchpad on the DS and the Wiimote on the Wii.

The penetration of a relatively untapped market - the "casual" demographic, due to a focus on simplified controls and arcade-style, multiplayer-orientated "pick up and play" games

Relatively low-priced hardware: the DS was 25% cheaper than the PSP and the Wii was around a third cheaper than the PS3 or the Xbox 360

Skillful marketing - aided in part by well-publicised hardware/game shortages

The 3DS doesn't have a new control system; instead, the novelty factor comes from the 3D display.  However, gamer response to this feature has so far been muted or even negative.  There's also the AR features but interest appears to have significantly died down once the novelty factor wore off.

Nintendo's appeal to the casual market should remain strong - they have a lot of casual-friendly IP, from Mario to Brain Training.  However, of the eleven "Nintendo-published" titles listed on Wikipedia, only three have been released and six do not have a confirmed release date, implying that there may yet be a significant wait until they're available.

There's still several months until Sony's NGP is released, making it difficult to do a true like-for-like comparison.  As it stands though, the RRP for the 3DS is significantly higher than it's current rivals.  To use some figures from the UK (based on figures taken from game.co.uk and argos.co.uk):

Admittedly, the incredibly steep discount being offered by game retailers makes it a bit more competitive - but at the same time, the scale of the discount implies that the game retailers are cutting margins in an effort to boost sales.

Nintendo have invested a lot of effort into marketing the 3DS, but the impact of this has been diminished by the delayed launch of the machine.  In addition, the 3DS's main "novelty" - the 3D screen - is something that can't be easily demonstrated on 2D media (print, TV); Nintendo has attempted to bypass this by ensuring plenty of demo-units have been distributed, but these don't have the same reach.  And perhaps ironically, unlike the Wii/DS, Nintendo ensured that there would be ample supplies of the 3DS on day 1 (and/or overestimated demand for the machine) and thereby lost out on the free publicity which would have ensued if it had sold out completely.

Project Cafe is rumored to have a touchscreen-based control system.  If true, then aside from the fact that this is no longer a particularly novel feature (e.g. iPad, DS, smartphones - even some laptops now feature a touchscreen display), this poses several questions: this may mean that the Cafe controllers may not be backwards compatible with Wii games (which would imply that you'll need to retain your Wiimotes, nunchucks - and possibly even the Wii itself to play your existing library) and depending on the size of the touchscreen, the controller may not be particularly ergonomic, especially for players with smaller hands. 

The Wii's most popular games can be played with just a Wiimote, by mimicking real-life actions (e.g. swinging a tennis racket, steering a car).  A touchscreen isn't quite as simple and may actually provide a more convoluted control experience: with limited tactile feedback, players may have to keep glancing between the TV and the controller to confirm that they're carrying out the correct action.

Wild guessing time: it's not unreasonable to expect Cafe to be on a parity with the PS3/Xbox 360; this would imply an RRP of between £199 and £299 ($249 - $399 in the US, given the usual european "import tax" markup).  However, this is unlikely to include the price of additional controllers - and with the Wii being just £99 ($149), casual gamers may well opt to stick with the older console unless Nintendo quickly phase it out of production

This partly depends on the controller: the Wii was easy to market, as you could show people waving the Wiimote.  The DS was easy to market, as the touchscreen is next to the main display, allowing you to demonstrate cause and effect.  It may not be as easy to advertise the benefits of a touchscreen controller which isn't next to the main display...