In the end, I really do think the socialist label would have doomed him.
The "socialist" label would have been easy to combat. He could just say: "Ignore the label, let me give you my position on the issues, and see if you agree". Most Americans do agree with Bernie on his core issues.
Democrats (and politicians in general) do better when they are not afraid of their own shadow, and project authenticity and conviction (this is Bernie's biggest strength, and Trump as well). If Trump ran a campaign that was "expected" by the media, he would have been apologizing for this or that every week, and would have ruined his brand and message. The key is political courage, and Bernie/Trump have it, while the vast majority of politicians do not.