For me, a console sells itself to me usually if it has one must-buy. Of course, the result is also that a game has to meet some pretty harsh criteria before it becomes a must buy.
But once a game reaches that status, I'm also willing to invest. Tekken has for a long time for me been the reason to own a PS1 as well as a PS2. Gran Turismo took over as the main reason around when the PS2 arrived. It doesn't mean that I don't love a tonne of other games as well, but certain games are worth hundreds of euros to me. There are only three machines I bought before I felt any must-have games had arrived, which are the Atari Falcon (yep), the Xbox, and the PSP. For the Xbox, I thought PGR2 might have been a must-have game, but I was ultimately disappointed by lack of wheel support - or rather, wheel support on GT4 was so outstanding that it crushed all benefits of the Xbox experience, never mind the accurate Nurburgring, 60fps and other stuff. As for the PSP, I definitely got my money's worth out of it, as I've been using it daily since the Japanese launch and have had plenty of great games. But the Atari Falcon and Xbox weren't so hot in my book - the latter was mostly good for playing multi-platform games a little more conveniently (HDD and such).
The PS3 is already a must-buy for me, with GT and Tekken/Virtua Fighter covered on day one, even if GT is only a demo without force feedback - you wouldn't believe how many hours I can put into perfecting laps on just one track, and this demo has one track, reverse, 20 cars, a drift mode, online leaderboards, etc. As long as the core gameplay experience is as good as GTs, then see the hours stack themselves
The 360 may become a must-buy for me if Forza 2 turns out to be a must-buy. Forza 2 can allow itself to be a tiny bit less hot also if Microsoft decides to support the Driving Force Pro, or even the Logitech G25 - in that case, the threshold for Forza 2 becoming a must-have becomes lower.
As of now, though, it's wait-and-see.
Anyway, this is just a long way of disagreeing with PARANOiA ...
Yes, one game can sell a console. As long as it is one of those games that you can keep playing for years, sure.