The Authority will use Eric's killing of Russell as a positive with the human population, where their PR has already taken the hit for losing control of a vamp. What they were willing to blame on Eric, and what they don't want coming to light, is Russel's other plans around overthrowing the Authority itself and his killing of the Magister. That would undermine them with the vamp community as well. If Eric suceeds in killing Russel, then they can pin the Magister's death on him as well. It helps that it's true of course, but not really relevant. Then they can use Eric as a poster child to the humans, and avoid a nasty issue with the vamp community as well.
I think that the Authority plans on making Eric a hero if he's successful. If not, they'd cut him loose and claim ignorance - that's what governments do all the time, no? They might prefer him to be a martyr than a living hero, but either way they'll be happy. Eric may go underground still - but I don't think it will be to hide from the Authority. He may need to be kept away while he heals, to avoid issues with Russel's followers.
Sophie Ann is more likely the one to get hit with lots of blame out of this, since the Authority knows of her v selling ways, and will want her out of the picture. Also, from a script perspective, I believe Sophie Ann is currenlty the only vampire outside the circle (Eric, Bill, Pam) that knows of Sookie's lineage. Killing her off would allow the writers to tidy things up a bit - and besides, this whiny TV show version needs to get killed.
So that's my prediction - Eric okay but needs to hide out for awhile to avoid retribution from Russel's group (and Sookie needs to take care of him, of course), Sophie Ann and Russell both dead.
And I doubt we've seen the last of Debbie Van Pelt...and we might see some additional set up for next season around the witches.
Eric.
There is no way in bloody hell that he dies - so I am curious how that is all going to play out.
Spoiler:
