Even though most people think he hasn't been entirely honest, Clinton's approval rating is at an all-time high. Looking more closely, the polls also show that Clinton's numbers went down only while his denials were carefully worded. However, once his denials became absolute, the approval ratings began to increase, rising dramatically after a State Of The Union address that refused even to acknowledge the scandal's existence. That said, the number of people who believe that illicit sex took place has remained fairly stable. So Clinton hasn't changed anybody's mind.
History supports the hypothesis.
Nixon, for example, was popular when he lied confidently. Look at the old newsreels. In the 1950s, he seemed to truly believe his Congressional opponents were communist fellow-travelers. Watch his face. By the time of the resignation speech, you could see in his eyes that even he knew there was hardly any point in pretending anymore.