This approach is used in California and other states and it generally works. The deposit is 5 cents and certain "healthy" drinks (juices, milk) are not charged. [If you live in CA, know all this, and are just arguing for a much higher fee - my apologies.]
Most middle-class people don't take household bottles in for the 5c back -- they recycle them in bulk for free -- but bottles in public areas are scooped up by poorer people.
Also, some people game the system in various ways, like importing out-of-state cans for the return value, or other types of fraud, which can be abetted by shady recycling firms.
So basically, a micro-economy was created with all its attendant functional and not-so-functional aspects. But the basic problem of roadside litter was largely solved.