It's perfectly natural to have doubts Winston becomes our next franchise QB especially considering we've only had one in Drew Brees. Unfortunately for the next guy, that is the measuring stick. I have my doubts as well but I think Winston has the tools to become the 2nd best QB in Saints history behind Brees.
The fact of the matter is that franchise QB's don't come along often. You'd be hard-pressed to name multiple franchise QB's for each NFL team. 49ers, Cowboys, Colts and Steelers are really the only teams I can think of that have had multiple franchise QB's. Some teams like the Lions and Cardinals have never had a franchise QB...not one that won anything of significance.
I don't actually think any real Saints fans are actively rooting against one of our own players and by extension our own team. I just think that those folks will point to the defense, the play calling, breaks in the game and pretty much anything else rather than acknowledging any positive plays by Winston. They still want the team to win. However, they want the team to win in spite of Winston rather than because of Winston.