You're not talking about the same thing. It's entirely possible to analyze worst-case scenarios without feeling overwhelmed, miserable, or doomed. Indeed the analysis will be better that way.
I never said negative thinking is overwhelming. I think it's exactly the opposite. Once you can come to terms with your worst-case scenario (ie. quitting and getting a job again when it fails), it frees a lot of burden and helps you work harder.
Think of it this way: planning for negative scenarios is generally implies that you're willing to deal with them. To be willing to deal with them, you probably think that you're capable of dealing with them.
Even though dealing with negative situations isn't kittens-and-puppies happy, it is solidly optimistic. That's the kind of positive thinking that helps you.