On days when it literally takes everything you can muster to drag yourself out of bed and into the shower, 15 pushups just aren't happening.
On other days it seems like a walk in the park to blast through 100... so I hear what you're saying. It's just that it's not always just as easy as getting through 15 pushups a day.
I've been in that same boat, being blessed with both bipolar and depression, and although just saying "hey some push-ups will do the trick" is perhaps a bit trivial I will add that even a tiny bit of exercise will help as it releases endorphins that are rather pleasant. Even on really fucking shitty days, I've tried to do a little work out. It's not a work out that will get me buff or anything but that's not the point. It honestly started as a healthy form of masochism for me...I loved the pain and it took my mind off everything else for a minute so I could focus on breathing and form. Even one or two push-ups, a long run...anything really...can help. It isn't a solution, but it's a relief and in the world of depression sometimes that's the difference between waking up tomorrow or punctuating a very short life.
I cycle for the same reason - forget the endorphins, they never really did anything for me. When it's just you and the road and the pain, you're free of all of it for as long as you can make your legs keep going. I imagine drugs do the same for some people, make them feel invincible or whatever, I don't know, I've never tried them and I have no wish for that kind of destruction in my life. The depression is threat enough to my way of life without compounding the issue.
But the bike, the wind in your face and the physical pain of the endurance is an escape from it all for as long as you can keep going.