As long as the total liability is decreased, then it's a solvable problem. We already have mandatory insurance in a lot of places. We could piggyback off that. It would involve some legislating and contracting and other paper-shuffling, but it doesn't seem impossible to just treat it as part of your insurance.
Heck, the insurance companies might even offer you a discount for turning your car over to a superior mechanical driver.
People may want to go after Google's deep pockets, and that's up to lawyers to figure out. I'm not a lawyer myself, so I can't really say how the ins-and-outs play out. For all I know, it may end up with Google assuming full responsibility, and you pay your insurance premiums to Google rather than your insurer. Google then turns it around to whatever reinsurer was really handling your insurance in the first place.
The transition would, I'm sure, be ugly, just because this is a litigious society and the rules encourage people to sue. Not to mention two political parties whose first jobs will be "what side of this issue are we on, and how can we make sure that the other side doesn't get what they want?", blocking any legislation. But of all the tech companies in the world, Google seems the one with the most practice at lobbying for a change.
Plenty of people will try to stop it, but there's also going to be at least some impetus to fix it, since it has the potential to save many lives and reduce traffic massively. (Automated cars can be much better coordinated and timed. Go watch humans try a zipper merge and you'll scream at all of them to get their incompetent hands off the wheels.)
That all depends on it working, of course, and we're some years from that. So it's not too soon to start working on the political theory of the new system. But a new system shouldn't be impossible. (Note: I am being uncharacteristically optimistic. My usual response to political things is "it's going to fail because the system is designed for inaction". Try again tomorrow and I may well find it impossible.)