FDR and Churchill were career politicians who just happened to be in the "right" place at the right time. FDR failed at the New Deal and all his anti-Great Depression programs and the war bailed him out. Churchill was bailed out by FDR into defeating Germany in WW2.
Lincoln was almost guaranteed victory in the Civil War because the North was so much bigger and stronger than the South.
I believe that certain leaders become overrated if they win wars. They are instantly turned into the greatest leaders of their time.
What do historians think?
I wouldn't say that FDR, Churchill, and Lincoln are considered great simply because they were "in the right place at the right time." Victory in both World War II and the Civil War was by no means inevitable. In fact, in both of those wars, there were significant periods of time where the side that eventually came out victorious seemed on the verge of defeat. Each of the leaders that you bring up had to do something to win the war, and considering the stakes of World War II and the American Civil War, that something often required courageous and decisive leadership that those individuals alone could provide.
It's also not always assured that if a leader wins a war, that he or she will be remembered as a great leader. George H.W. Bush, for instance, is widely seen as a slightly-above average president, despite an overwhelming victory against Iraq.
As a sidenote, I'd also like to point out that there is still some disagreement about the impact of FDR's New Deal policies--it's certainly not agreed that those policies failed. In fact, the majority of historians say otherwise.
Question for people who understand economics more than me: can the improvement of the economy following WW2 be viewed as a vindication of the New Deal rather than as something which "bailed them out" after their failure? In other words, were FDR's ideas sound, and it was just the political capital brought about by the war which allowed him to spend the amount of money on the workforce which was required?
The way I see it wartime spending was very much following similar principles to New Deal spending, where the federal government employed tons of people and built up the infrastructure, with the main difference being that the amount of money spent employing people in WW2 went way beyond the amount of money spent on the New Deal.
Again, I'm know very little about economics, so I'm probably way off base. I just always thought it was odd how people say, "the new deal failed, WW2 saved the economy" when the spending being done in WW2 on the US workforce seems sort of like the new deal on steroids.