I think there's a hint the manga [SPOILER], when Saitama loses to King in a video game, and King says its because his fighting style is "too predictable". Then later, One Punch man one shots a giant centipede and he says he feels relieved after destroying it (with his simple and predictable punch, although it is worth noting that it was a 'serious punch') and King is surprised that Saitama was still mad from the battle.

Taking everything into consideration, what I'm trying to say is that Saitama may very well have some hidden source of power (like Goku) and just doesn't know it. But instead of coming from pure determination, it manifests out of him becoming as 'simple' and therefore as 'predictable' as possible.