Is a first class medical to be an airline pilot eventually possible?
The section 

Decision Considerations - Aerospace Medical Dispositions
Item 47. Psychiatric Conditions

From the FAA's website has a lot of the information for you. This page on SSRI's specifically has even more info to read up on. If you burrow down you will find a lot of worksheets and AME advisory papers most of which ultimately state 


  Requires FAA Decision/Submit to FAA for approval 


This basically means that the AME can not make the decision and its up to the FAA directly. That being said there is hope and they do make a path pretty clear for you to take. 

In any case if you are tapering off a drug it may be best to wait until you are off it completely to go see an AME. The FAA seems to be much more cut and dry on current usage and far more "case by case" on historical usage based on the way the regs are written. 

You may also want to take a look at the regulations here