While there is no doubt that Diablo 3 can work on a console, it would have to be a dumbed down version, by neccessity.
First off, for classes such as monks, moving and attacking at the same time is agodsend. Separate controls for movement plus aiming would suck for a monk, it's much easier to play when these are combined, there is no "aiming". It's the ultimate dumbed-down toon, and I'm proud to play it. Literally I just point where I move and attack at the same time holding down the mouse button, and everything is taken care of. I don't use WASD, everything is done with the mouse. This will translate very well to consoles with a gamepad. Other examples would be WW barbs and CM wizards. All three of these classes, you could make an argument for an auto-attack feature (I wouldn't have to hold down the mouse button anymore!), and just focus on movement.
Now, I think we can all agree that any game where you need to quickly (and/or accurately) point to any part of the screen, a mouse+keyboard combo is superior to a gamepad. Almost every FPS like Call of Duty is better with a M+K because of this. There are certain aspects of Diablo where this is required. Ranged classes like demon hunters being one. Picking up loot would be another. Equipping and gemming items would be a third, although this can be mitigated somewhat. This is where a console version of Diablo 3 will suffer compared to the PC version.
Lastly, there of course is text inputs, where a keyboard is just necessary. In Diablo 3, this means the Auction House and chat windows. I just can't imagine doing either of those things with a gamepad. You could say "well, you could get a keyboard for your console", but let's be realistic, 1) I bet less than 10% of all users have a keyboard hooked into their XBox or PS3 atm, and 2) if you are like me, most gamers, we play our consoles in the living room, on a couch, I'm sure as hell not typing with a keyboard on my lap. Hence, I think, one of the reasons for the poor adoption of keyboards with game consoles.
So the PS4 version of Diablo 3 will probably have no chat window functionality, and the auction house will likely be a clumsy mechanic, with "smart-fill"...type in "ar" and you get "archon". Normally this wouldn't be a big issue, except that in Diablo 3, the Auction House is a HUGE part of the gaming experience, for better or worse.
Lastly, although I realize that PS4 and PC versions will likely have different server clusters, I think that's unfortunate. I would never buy the PS4 version having the PC version myself.....however, if they did share servers, and my toons would be available on the PS4 because I would be using the same Blizzard account....that would sway me to buy the PS4 version so I could occasionally just play the "lazy" version on my couch. After all, I would still be able to advance my toons.