A lot is going on when Jon is stabbed at the end of A Dance with Dragons. He has just received the so- called Pink Letter from Ramsay Bolton and has declared his intention to break his vow and ride south to confront Ramsay. The wildlings have enthusiastically supported him and this seems to be the last straw for many in the Watch. Jon has let the wildlings pass through the Wall in exchange for committing to fight with the Watch when the Others come. It's a simple matter of needing more men, and also to save the wildlings- but Bowen Marsh and the other malcontents don't see that. They think the wildlings are the enemy, and Jon doesn't do a good job of communicating his rationale.
The interesting thing here is Castle Black is full of wildlings at the moment and also of southern men, the knights and soldiers loyal to Queen Selyse. She was left at Castle Black when Stannis went south, and indeed the Pink Letter asserts that Stannis has been defeated and that Ramsay wants the queen turned over to him, along with Shireen and Melisandre. Not only that but just before Jon is attacked one of Selyse's knights tries to get to Val, the wildling being guarded by Wun Wun the giant. So everyone is drawing weapons and the place is a tinderbox.
Amidst all this Jon is stabbed repeatedly and presumably killed. What will happen next? Well there could be total chaos between the Night's watch, the wildlings and the queen's men. The situation is more complex and volatile than depicted in the show. The wildlings have just agreed to follow Jon and he and Tormund are sort of BFF's at the moment, so they may not take kindly to Jon being stabbed. The queen's men (and the queen) don't seem to like Jon -but Melisandre is the true power behind Selyse. If she commands the men to protect Jon or orders Selyse to do so, I don't see Selyse defying that.
And you have Wun Wun. There's a real chance that the giant goes on a rampage. But the real wild card for me here is Melisandre, without a doubt. Selyse defers to her, probably fears her, and I think Melisandre will not be pleased to see Jon killed. There could be a bloodbath at Castle Black.
And we're not even touching on how Jon will come back (the assumption being that he will). This has all been settled on the show but the books will almost certainly take a different path. It seems that by killing him the Night's Watch has probably released him from his vows, enabling him to go south. But Jon is the only one thinking ahead to the true threat- the Others. Will he take Winterfell enabling the defenders to have a base to stop the northern apocalypse? Or will he come back to lead the Watch, if it even still exists?