The car's themseves may be more cost efficient to run, around $0.30c/litre equivalent, but they are far from efficient when it comes to CO2. For example, a lifecycle analysis of lithium batteries commissioned by the Swedish government indiscates that for a Telsa Model S (driven average annual distance for a private vehicle) , it would take approximately 8.2 years for the battery system to have a CO2 footprint similar to that for a hydrocarbon fuel system. After 8.2 years there is a CO2 saving. I understand the figures are based on average electricity generation mix for markets Telsa supplies it cars to. There have also been studies by the Chinese and other countries which have had similar findings.
Lithium batteries have a very high embodied energy if the whole lifecycle is considered such as mining, lithium processing, battery fabrication (such as that planned in the Telsa Gifafactory) and material transportation. Telsa has indicated that it plans to have its own lithium battery plant fully powered by renewable energy in the future, but it is yet to be proven.
I believe that @TheBBG solution may be more on the mark as hydrogen can be produced when excess electricity is generated (when supply exceeds demand) and could have a significantly lower carbon and environmental footprint (if environmental impacts of lithium mining and processing is considered). It's primary inputs for manufacture are water and electricity (which could be from low carbon sources...or even nuclear since nuclear is the least volatile electricity generation source and may produce excess electricity during periods of low demand).
Hydrogen also overcomes the tyranny of distance problem through quick refuelling, a currently limitation to lithium battery systems.