How long can I leave a body panel(or entire car)in a state of primer.
I need to do this for a while.
I will do all bodywork and then prime.

Well...it depends. If the parts are in a warm and dry area you might be able to go as much as 6 months, maybe longer. If it's in a damp area you will be looking at about 1 week, maybe less. This is not etched in stone and can vary.

My buddy has had his 63 Impala in primer for almost a year now. Proper covering or leaving it in-doors, it should be fine for a long time.