According to the film's director, Peter Jackson, Smaug wasn't sleeping sleeping, he was just cat-napping. Bilbo moving the cup (and causing the dragon's head to become slightly uncovered) was sufficient trigger to return him to full consciousness within a few seconds.
Jackson: Revealing Smaug was a moment we...
Boyens: We used the gold cup. Which I loved. The homage to the book.
Jackson: The gold cup has a bit more story in the book, but OK. And I love the idea that too, that it's an homage to the end of the first film. That we're replaying the end of that first movie. Now the dragon, he's just like a big cat. He nuzzles into warm cosy things. Gold must have quite a good heat transference. And I mean it's like he's warm in gold. ... It's like the dragon is so comfortable in gold. He just adores it. It's like on of those TV commercials for a feather mattress one of those scientifically designed mattresses, well, he's got his. It's all these coins and he's just very, very happy there.
Desolation of Smaug: Official DVD Commentary
