I imagine the government would have to set up a strict requirements and tests, and then once licensed the vendor would be immune from suits unless gross incompetence or malice could be proven and that they would also then benefit from an insurance pool to compensate/benefit those injured due to the system with some sort of cap or limit to the payouts.
After that was in place, I'd think government and businesses would jump on it to avoid being sued for their employee's driving errors or for simply having their logo on the vehicle, not to mention long term cost savings of not having a human driver (no more wage, insurance, or tax costs) and therefor not needing a cabin and add 24/7 driving and better fuel economy (from no a/c and fuel saving driving patterns). Heck, UPS, FedEx, and the USPS could all redesign their vehicles to carry more while making it easier and even faster for the employee to deliver the mail or packages.
I'd also think those that can't or shouldn't be driving would also be quick to jump on it. For instance, once you had a system like this in place, I'm sure you'd see laws sprout up prohibiting anybody ever guilty of DUI from using a human-driven vehicle. Seniors that can't drive or would rather not will love these cars as they would give them freedom to go anywhere any time, and the people will love that they aren't driving, perhaps leading to lower maximum driving ages. I'd imagine minivans that had no "front seats", designed more like a limo, would be extremely popular with families. Make a sedan designed like that, with rear facing front seats with a built in table and power outlet, and I'm sure most commuters would jump on it. New drivers would simply be used to it by the time they could even apply for a license, so the number of people against the concept would naturally lower every year.
So those that wouldn't want to give up the control could hold out, at least until you end up with such a huge portion of cars driving themselves, that the population starts limiting human driving (more expensive and difficult to obtain licenses, automated-only rules for freeways, tolls, etc) or driving around them becomes too annoying (I enjoy driving, but if every car was going the posted speed limit, and I imagine those limits would only go down, it would get old very fast!).