It would be possible, but improbable. You could do it on a 360 or PS3, but you would need to be able to render everything at 120fps. In other words, the game would look twice as bad, and that gameplay feature would probably not be enough to sell the game(s) because of the lower quality. This would apply on any console, past present or future. Any game you run will have to look twice as bad in multiplayer as the singleplayer version.
So, yes, it's possible, but not likely to be implemented.
why do you need 120 frames? shutter glasses? you really only HAVE 30 fps per person anyway, virtually NO console game runs at more than 30 fps. so are we assuming shutter glasses? like those from nvidia? imo shutter glasses are utter rubbish as a concept from the start, the glasses themselves are impractical and if you think about it the approach basically converts a nice lcd, led or plasma back into a **** CRT display.
theoretically you only need 60 fps rendered, on a TV that works with polarization. instead of 2 pictures for one viewer you send out 2 pictures for 2 viewers, simple, each player's glasses have one kind of polarization on both lenses.
the real problem is RAM, video- aswell as normal: for 3D you just need twice the framerate but it stays the same gameplay whereas with two players you have potentially twice the amount of objects, textures etc filling up space. i mean i'm assuming this "coop-console" would have singleplayer titles, too. in MP everything has to be present, you can't do much streaming, no tricks. but in SP players would have to be able to take different routes through waaay bigger environments, even in a linear game they couldn't be forced to stick together, that would be lame and take away the point of such a system.