I see the Revolution being a success because its not trying to compete directly with Sony and Microsoft's systems. Nintendo has a different idea of what videogames should or could be, and while that may not cater to the hardcore gamers who spend hours a day on X-Box Live, I do think they have a very good chance at attracting an audience who has never played a videogame other than Tetris.
Look at the success of Nintendo's DS. I know sorority girls and 50 year professionals who play DS because it has intuitive control and some extremely fun, creative games in its library. I see the Revolution aiming for the same broad appeal, but with an even more intuitive and design inspiring form of control than the DS's touch screen.
You must also not forget the huge price difference between the Revolution and its "competitors." The Revolution will be less than half the price of XBox360 and PS3 making it much more appealing to casual gamers and as a second system for the more hardcore.
Finally, the Virtual System will definitely be an appeal for every nostalgic person who enjoyed the 8-bit and 16-bit era. If the success of the the rereleases on GBA or the popularity of emulating is any indication, then this could be a huge market.
The Gamecube has failed because it offered nothing that the XBox couldn't already do better. Your only incentive to own one was Nintendo's own titles (which had some slouches and some masterpieces this generation) and the Resident Evil games. With the Revolution, and to a lesser extent the DS, Nintendo is attempting to broaded the idea of what constitutes a video game with the hopes of broadening their audience in the process.
I do think the lack of HDTV support could hurt it down the line. Afterall, isn't broadcast TV supposed to change over by 2009? Still, as the old saying goes, "its not what's on the outside, but on the inside that counts." In the end, the winner will be the one that inspires the best games.