Congress has the lowest approval rating in history - BOTH parties. The People do not like the politicians in Congress. That said, it is common knowledge that neither party in Congress has any love for Gingrich. That tells the People that maybe Gingrich is the man they are looking for. It's kinda like that old saw about "The enemy of my enemy is my friend."
The People dislike Congress. Congress dislikes Gingrich. Hence, Gingrich is the guy they need to beat Congress into line (because that is what it will take).
So, when either party of Washington insiders trashes Gingrich, it actually HELPS him
It shows that Gingrich, though he knows his way around D.C., is still an outsider, because he is an outsider politically.
And that is what the folks are looking for - an outsider who has been inside long enough to know how it works and can get in there and repair some of the damage.
The fact that he is also the only one who can out-debate Obama doesn't hurt, either.