How much weight can my garage's ceiling joists support?
It should make you leery. Playing around with a wood beam calculator I had to trim loads down to 7 lbs per square foot to get any of the solutions to come up 2x6 for 20 foot span and 16" spacing. That's not even light storage (by my definition.) It's not even a residential attic with no storage by more official definitions (10 PSF) nor an attic with storage by those (30 PSF)

Either leave it alone or hire a civil/structural engineer to develop a plan where you'd either refit the roof structure (effectively turning a rafter and joist arrangement into trusses, if that's practical, by adding web members) or place a properly sized and supported beam down the middle to cut the span in half. In short, if you want storage up there, it will cost a bit more than a set of stairs.