For me it's tied to the 360. It has to have backwards compatiblity (maybe not 100%, but certainly better than we had in the XBox to 360 transition), and just as importantly backwards compatiblity with 360 DLC. The second one seems like it could be a difficult situation. No idea what kind of deals, say, Harmonix has in place that would or wouldn't allow them to make songs work on another console.
I know that a lot of people write off backwards compatiblity as something that doesn't matter after a year or so, and I do agree somewhat. But the XBox and 360 are in completely different boats. Catering to the XBox audience when the 360 showed up wasn't totally necessary since the XBox didn't exactly set the world on fire. This time around the console was extremely popular and has had an incredibly long lifespan, and it seems crazy to me that they wouldn't do everything they could to try to make it easy for their current customers thinking about plunking down another $400 (or whatever) by reassuring them that this can completely replace their 360 with no worries about giving up the games they already have.
Not to mention the industry has changed massively since the last console transition. There are a lot of people with a TON of money invested into content that is tied to their consoles that they can't just go and dump off at Gamestop. I know the attitude of the game industry could just be "fuck 'em, we got their money, gave them what they paid for, now it's time to move on" but I don't think it really can be as cut and dried as that with the way things are now. I'm probably wrong but I'll maintain foolish hope that everything will carry over, at least for now. I'm going to be incredibly reluctant to buy ANY upcoming console if I'll be starting over at zero. I can't be the only person who feels like between games, special editions of games, online services, and DLC they have sunk more money into this current generation of consoles than any other (for me, dating back to the Atari 5200).
Just as importantly, MS needs to make up for the 360 launch by showing customers some good will and proving that they have solid hardware. Gamers certainly have short memories and are willing to forget just about anything, but I still have a feeling a lot more people than normal will be taking a wait-and-see approach to see if we get another hardware failure debacle like last time. I know I won't exactly be standing in line at midnight...I'll let others be the guinea pigs.
Oh, and although it will never happen since we're not ready for it yet...a digital distribution-only console would be something I'd avoid completely. I want my discs.