What I liked at E3 was how they said it wasn't a "next generation" console, but a "new generation" of consoles. In Standard or Enhanced Definition, the Wii will be reasonably competitive with the 360 and PS3. I think it's good to differentiate this point with Wii, because otherwise people will simply say "it's not as strong" -- it's not a competitor for your "first console" position if you want the high-powered specs. But I'm not going to spend $1000 to get a 360 Premium package and a non-gimped PS3 -- I'd rather spend the $800 for PS3+Wii or the $600 for 360+Wii IF I was planning on buying two systems. Anybody who buys all three systems and complains about not having money, I will laugh at, because they're a little...
Iwata is aware that in the traditional market, Nintendo has been losing footing ever since the NES, and especially since the SNES. If you look at Sony and Microsoft, they're both already half-assuming people will get a Wii along with their respective consoles. They already see that Wii isn't a competitor, and are endorsing it to their market because of that. Nintendo established that it's not trying to be competitive, but to expand the market. The people who get a Wii and not a 360 or PS3 are who Nintendo is targeting as their new market, and they weren't going to buy a "next generation" console anyway.
My favorite quote was at the end. Iwata said that they want a system people will turn on every day. I know what he means about gaming sessions around major releases and then not playing for a while. I live it. Especially on my GameCube, but also on my PS2. The only thing that would bring me to PS2 on a daily basis would be Final Fantasy XI, and right now only because of the recent expansion pack. Animal Crossing doesn't even do it anymore on my GameCube (but it does on my DS). I'm waiting for the Wii eagerly.