I can look up the study if you want but a little under ten years ago the Dutch government had a full well-to-wheel analysis done to figure out the advantages (as far as pollution goes) and it includes the break even point for their chosen EV (a classic Nissan Leaf.)

IIRC the break even point when powered by renewable energy was about 60k kilometers.

Depending on where you live and your driving habits that could be seen as a lot, but considering that after those ~40k miles every mile can be considered 'clean' I don't think it's all that bad.

Edit:

Source in Dutch: http://publications.tno.nl/publication/34616575/gS20vf/TNO-2...

TL;DR: Assuming a car lifespan of 220k km (136k miles) and including emissions for fabrication, repairs, etc. emissions will be 70% lower for an electric vehicle powered by renewables. When powered by non-renewable energy it's still 30% less total emissions than a regular petrol car. Other than that you also emit less of various other pollutants. And (personal opinion alert) it's just a way nicer drive ;-)