Kill the 360, not a chance. Kill the X-Box brand highly unlikely!
Halo was a monumental franchise and will likely continue to be so. Think for example what Nintendo did with Pokemon when GameFreak couldn't deliver on home platforms. They created Pokemon Company to take over and bring Pokemon games to the handhelds. In the same way Microsoft has created a new company soully to handle Halo. The Halo franchise will continue to sell and probubly be a big selling point for the next X-Box.
Bungie is over rated. Keep in mind until Halo all their other franchises flopped. They failed to create a single system selling game. No AAA+ games there. Some developers go a life time and only produce a single outstanding franchise. Also the co-founder of Bungie left to found WideLoad and several other key employees have disembarked. The studio isn't the same studio that created Halo. I suspect several other staff might be lost in the transition much like when Nintendo lost Rare.
So a studio lacking the same visionaries who created Halo. A studio with only a single big hit franchise. Why would the loss of that single studio mean doomsday for Microsoft? Infact Microsoft has closed several big important studios like Ensemble for example and they haven't really suffered. Microsoft will simply find fresh meat and create new studios to churn out more new IP's.
Also keep in mind any title Bungie does release for Activision will be cross platform. With Bungies history you can almost guarantee their games will still show up on the NexBox. So with their titles now multiplatform why would that kill Microsoft? The Microsoft user base will probubly continue buying the Bungie games on the X-Box and little change should occur!