I think it is not at all known to the average English speaker. Moreover, unlike the average English speaker, I work with EU affairs every day, and I don't know what a Eurobarometer is either. As ever, Wikipedia comes to the rescue. http://en.wikipedia.org/wiki/Eurobarometer
Thanks very much to you both! I myself know what the Eurobarometer is, thanks to Wiki, which I'd already used! I'm translating it into English from a foreign document and wondered if it required clarification for an English audience. I suspected it would, but wanted some confirmation.