I don't think anybody knows. Corbyn's supporters are pointing to the large membership increase since the leadership contest started, and opponents are arguing that he will alienate various groups of people. I guess that the polls will be watched for a while, to see which way it's going. Corbyn is having a tough time with the media, but again, I don't know how much that will count. If Labour start to sink badly in the polls, then his time will be short, I would think, although I'm not sure that Labour led by anybody else will inspire anybody. Of course, Keir Starmer lurks in the wings, but he is too new, I would think.
If Blairites cross to the Tories, that is rather giving the game away!