I think my problem with Dany early on (in print) was that it felt like a secondary story; it's off in this far corner of the world, and there's so much going on elsewhere. I just wanted Martin to get back to the interesting stuff on the other continent. There was also the whole Conan vibe to it, and initially that felt off to me in the middle of the medieval sword and sorcery stuff going on across the sea. The whole subplot seemed detached, although I knew rationally that it wasn't.
On the show though, they've made a point of emphasizing it and making it seem as important as everything else going on right from the very start. I'm fine with it.