Problem with solar is that its hard to run cars on it. Fix that, and we're walking in tall cotton.
Assuming 3 kWh / mi (less efficiency than your number) and driving 12,000 mi year for a consumption of 4,000 kWh / year.
In Phoenix, Arizona (one of the sunniest areas of the USA, 1 kW of solar PV will generate about 1600 kWh / year (data from PVWatts)
In Seattle, Washington (one of the least sunny areas of the USA, 1 kW of solar PV will generate about 1000 kWh / year.
So in Seattle you need about 4 kW of solar PV and in Phoenix you need about 2.5 kW of solar PV. Solar PV is only around $4 / W or less for a residential install (without tax credits rebates or other subsidies) and will last at least 20 years. So for 20 years of driving or 240,000 miles, your energy will cost between $10,000-$16,000, or about $0.04-$0.07 / mile which is cheaper or equal to the cost of fueling a 50 mpg Prius!
Conclusion: Driving on solar power is possible today and cheaper than gasoline!