The most likely way this is going to go down is Congress is going to pass the extension again and it's going to go to the Supreme Court. I would consider the probability of any other outcome pretty low.
The US legislative process lives and dies on building alliances and horse-trading. A word from the President and/or his/her promise of future help in other matters is hugely valuable. A law going through Congress and a law going through Congress with support from the President are two very different things in practice, and would be disingenuous to say that's not the case.
It used to, back in the day. That hasn't been the case for a while in today's extremely partisan environment where compromise is now a dirty word and presidential support for something makes it less likely to pass given the hostile congress that will remain even after Clinton wins.
That's all a big show on wedge issues. On topics that matter to people with money (bankruptcy laws, banking laws etc), it's just business as usual. The DMCA was passed in a similarly "partisan" environment. Don't believe the hype.
As such, all current candidates, with the possible exception of Sanders, would probably consider signing a copyright bill routine (Lessig isn't a candidate anymore).
What makes you think so? This is one of my greatest fears of another Clinton presidency.