The biggest reason why it took a long time for cars to replace horses was high price (simply stated: most people couldn't afford a car even if they wanted one) and lack of infrastructure (it takes years to build roads).
We already have the infrastructure and the price will favor self-driving cars.
The laws heavily favor safety in cars (not everyone likes seat-belts and yet we have laws requiring people to use them; we have laws banning using a cell-phone while driving, driving while drunk; cars have to build in a way that withstand crashes etc.).
As long as it can be demonstrated that self-driving cars are safer (and they are), there will not only be pressure to allow them but to require them and eventually ban human drivers altogether.
Once the self-driving cars are allowed, the lower price and greater convenience will make it a blockbuster. I don't want to own a car, I don't want to operate it, I just want to get from Mission to SOMA fast and cheaply and self-driving cars will be able to offer that.