Filler is the one thing that ISN'T going to happen (as hillarious as it would be), simply because it's too expensive to make the damn things. Unlike Naruto, this isn't some mid-tier mass-market anime; this is one of the most expensive HBO projects to date. Hell, the second season was debatable (for a while) despite the solid success of the first one simply because it cost so much to make.
What is most likely is that the show will go on a hiatus. Martin did give his notes to the makers of the show, but that was as a contingency for his death (Martin not being particularly young at this point). I doubt he'd let them use the notes to essentially spoil his book(s) ahead of time. And a hiatus would be a pretty bad thing, as key actors might float away to other projects and need to be recast.
That being said, it might not come to that. The current season is mostly the second half of Book 3, with some snippets from Book 4. They'll be able to squeeze at least 3 season out of books 4 and 5, maybe even 4 seasons. Martin's next book will be coming in the next year or two and will be "milkable" for a season or two. This'll leave him 3-4 years to get the last book out, which he might be able to if he stopped faffing about so much on side projects (he himself admitted that he was procrastinating the whole thing).
And personally, I can't wait for the Mass Effect 3-level of disappointment that the ending of the series will cause, because at this point GoT/ASoIaF is so big nothing will live up to the hype...