Currently the biggest challenge of UBER is regulatory - cities are fighting it tooth and nail. One way to exert strong political pressure is to offer a real breakthrough new service for the mass population(and not something like UBER which is an incremental innovation targeted for a small section of the population). This also fits with the breakthrough mentality shown by google's leaders.
Such service could work like UBER for public transit[1], basically enabling people to share rides with multiple other people while decreasing the costs significantly and maybe making such a service an viable alternative to private transportation. Such an offer would be hard for politicians to resist for long.
One key to enable such service at scale, is access to plenty of people and their real-time travel data, and having an ability to offer them an highly targeted ad + route + service. That sound perfect for google+UBER. Like a huge market they're positioned perfectly for.
[1]Previous HN thread: https://news.ycombinator.com/item?id=7391885