Doris Kearns Godwin, author of two highly regarded studies of the Lincoln and Roosevelt administrations, offers 10 personality traits of great presidents based on her life time study of Presidents, beginning with her working with LBJ.
1. The Courage To Stay Strong: "A President needs the ability to withstand adversity and motivate himself in the face of frustration."
2. Enough self confidence to surround yourself with first rate people: "Good leadership requires you to surround yourself with people of diverse perspectives who can disagree with you without fear of retaliation."
3. The ability to learn from mistakes: "To lead successfully, you must be willing to acknowledge and learn from your mistakes."
4. A willingness to change: "Conditions change, and Presidents must respond."
5. Management skills (what she calls emotional intelligence): "A President must encourage his closest advisers to give their best and remain loyal."
6. Self control: "Great leaders manage their emotions and remain calm in the midst of trouble."
7. A popular touch: "The best Presidents have an intuitive awareness of public sentiment, a sense of when to wait and when to lead."
8. A moral compass: "Only strong leaders have the courage and integrity to follow their convictions when the risk of losing popular support is great."
9. A capacity to relax: "FDR held a White House cocktail hour every evening. Its cardinal rule: Nothing was to be said of politics or war... Lincoln possessed a life-affirming sense of humor and a legendary ability to tell long, winding tales"
10. A gift for inspiring others: "One of the key qualities of a great President is his ability to communicate national goals to the people and to educate and shape public opinion."
You can read about these attributes in more details and with examples from Lincoln and Roosevelt in her article.