At the end of the day, I'm not sure how much impact a manager has - I'm sure there's an impact but it is difficult to quantify.  That said, while I'm not crazy about Gibbons' in-game decisions, a manager doesn't necessarily have to excel at in-game strategy to be successful.  

Folks (including myself) will point to Gibbons' bullpen management and his construction of the lineup, but if you look down the right sidebar at our brother and sister SB Nation sites, those are the same criticisms that every team's fans has for every manager.  While I have been frustrated with Gibbons' endless tinkering with the lineup for what seems to serve little purpose, I think we can all agree that replacing Gibbons isn't going to end those criticisms.  

What it comes down to, in my opinion, is this.  The one thing a manager absolutely has to be able to do is have the respect of his players and project on the team an on-the-field unity of purpose.  I've played for managers that did this and ones that did not, and the ones that did consistently got performances out of their players that exceeded expectations.  

Whatever ability Gibbons may have had to lead this team no longer exists, in my opinion.  It's unlikely it will return.  When that happens, you have two options: change the players, or change the manager.  J.P. has said he's sticking with the players, so it's time to let Gibbons go and see what someone else can do.  

I do usually oppose firing a manager in the middle of a season, but I don't really care either way whether he goes now or in the offseason.  If the Jays don't have someone in mind to replace him, let him serve out the year or ask him to resign (with pay, of course) late in the season and then finish it off as a lame duck.  It's time for someone else to have a chance with what seems to be a more talented core of players than their record indicates.