I think people might be jumping to conclusions a bit. I really doubt it means that the console would be a paperweight unless it's connected to the internet. More likely it will be an 'always on' device that never really turns off and I can't imagine it not having an 'offline' mode for gameplay, probably in the same mold as Steam. You would just have to register the game online initially.
Of course, Steam's offline mode is incredibly annoying at times, so even that might suck pretty hard.
Those things wouldn't keep me from buying one, though I can say with little doubt that the amount I'd be willing to pay for a new game would be much, much less. Day One buys would be few and far between for me. Without being able to recoup some of my purchase cost by trading or selling, I would probably become a bargain bin shopper.
Still, I kind of doubt all that will happen. It would be the same as abandoning any market that doesn't have widespread internet access. Seriously, I live in the US, and I have friends who don't have access to cable or DSL broadband services.