And in the books, they did. Many deserted at that immediate moment, while others carried out the orders they were bred to follow. Some clones helped their Jedi Generals to avoid execution. These clones were bred completely loyal to the Republic, not the Jedi. Their directives were drilled into them over and over until it became as reflex as breathing air. And remember from the movies, Yoda states that the Force and visions of the future have become clouded due to the presence of the Sith, making it more difficult to sense the threat before it was too late. While the Jedi are powerful, they aren't aware of every conversation uttered by every sentient creature in the Galaxy, so one man uttering the words, "Execute Order 66," would not have been sensed by any one Jedi, unless they were looking for it, perhaps.
At least, this is all info from the books and Star Wars lore up til now, as well as my interpretation.