I will never under any circumstance pay anywhere close to $20 to rent a game for any length of time. And I'm a person who wastes a lot of money on stupid things.
The only thing I could think where $20 to rent a game would be even a consideration, would be for a lifetime rental. Say you pay $20 to "rent" God of War 3, and you can play it anytime you want, any day you want, for the life of the PlayStation Now service.
I would compare that to what I do many times now, I buy a game new for $48 (thanks Best Buy Gamers Club Unlocked) and turn around and sell/trade it for $30-$40 within a couple of months. I basically lose about $18 to play the game for a few months. So I could see people pay $20 to have the game forever, or at least be able to stream it.
HOWEVER, this whole scenario would be in direct competition with the PlayStation Store and retailers, so I doubt that will ever happen. BUT, wouldn't a simple monthly subscription fee also be a direct competitor? I guess it just depends on how much the big publishers get in a kick back.