EDIT also, perhaps against better judgment, i'm going to throw a possibly inflammatory remark out there and say that the big-O thing is really not that difficult or important (although i suppose that it's important that it not be difficult). what i can see taking some skill/experience (which i totally don't have) is knowing a bunch of algorithms and being able to consider the time/space tradeoffs of the algorithms you already know quickly. being able to prove the time-complexity of some new algorithm is good, but, sadly, perhaps, i don't think most companies hire people to do that.
and since you're imagining rather than being certain, that means people continue to downvote without comment, and i continue to cheerily object to that.