Regardless of what you thought of his politics, Clinton had charisma. What's charisma? You know it when you see it. It's the type of person that can best be explained in idioms. They light up the room. They draw people to them like moths to a flame. Even people that are fundamentally opposed to a charismatic person quickly find themselves changing their position once they meet him or her. They have "It". That intangible thing that makes someone a star.
Can you learn charisma? Sure, you can learn how to really listen to people, how to remember people's names - but you have to already have a genuine interest in people. Can you learn that if you don't possess it already? I'm not sure.
What was the key to Clinton's success? I think it was best described in an article I read. A man said that even when he just briefly met with Clinton, Clinton made him feel as if he was the only person in the room. A person I know who briefly met Clinton reported the same feeling. "He looks at you like you are the most important person he's talked to that day. Even though you know you're not, you still feel like you are."