Based purely on their significance (how they changed things in ways other men may not have done so) ....
1. FDR - 12 years as President gives you a lot of time to make changes. His social programs and foreign intervention changed America and the world as a whole.
2. Thomas Jefferson - 2 words, Louisiana Purchase (literally doubled the size of the country). 2 more words, West Point (gave America its own training center for a professional army).
3. Abe Lincoln - Some men would have let the nation split. Some men would not have excercised emmancipation. Like him or not, he changed the nation.
4. LBJ - Great Society, escalation of Vietnam, civil rights. During LBJ America grew up.
I think you need to reread the question.
Ugh ... you're right ... my bad. Bad day for me. Let's try over, eh?
1. FDR - Reasons previously cited
2. LBJ - Reasons prevously cited
3. Truman - His decision to use the A-Bombs dramatically altered the world. Throw in the Marshall Plan, United Nations, handling of the Cold War, decision to hide certain Axis Power scientists, recognition of Israel, and his handling of Korea and you see he had a dramatic impact on history.
4. Nixon - Opened China, ended Vietnam, but also by getting busted over Watergate he changed the face of American politics.
