He probably would've had a better chance when he was holding the saber inches away from his neck.
Seeing how easily Dooku sidesteps all of Anakin's attacks—he did so from the behind on Naboo—I don't see how Palpatine can't just sidestep him.
If you look at the reveal scene, you see Sidious moving his left-hand fingers in his sleeve immediately after Anakin ignites his saber. Could he be reaching for his saber?