I doubt it.
We tend to view both Lincoln and FDR through the lens of present-day sainthood, but if we saw them as their contemporaries did, they might never have received our nod.
Yes, I know Lincoln was a Republican, but the parties have swapped places, so I think he would have been a modern-day Democrat.
Anyway, Lincoln was a one-term Representative, who had just lost a highly visible Senate race. While he opposed slavery as a threat to everyone's freedom, he was not the first choice of abolitionists. William Seward and Salmon P. Chase were considered far more reliable and militant on this issue. Besides, they were able politicians representing powerful states, while Lincoln was a part-time railroad lawyer.
FDR, meanwhile, began his career as a Wall Street lawyer, and then parlayed his name to a State Senate seat. While he developed a reputation as a reformer fighting Tammany Hall, he would later reach deals with that powerful organization.
He became Assistant Secretary of the Navy in the Wilson administration. He brought some efficiency and professionalism to the department, but flopped in his efforts to run for the US Senate and the Vice Presidency.
He won the NY Governorship with the backing of Al Smith in 1928. His first term was undistinguished, but after the Depression hit, he pushed some policies that would become part of the New Deal.
It's worth noting that both Lincoln and FDR were considered, at times, as lightweights and sell-outs. They both had reputations of avoiding conflict, and even saying contradictory things.
Lincoln dragged his feet on emancipation. Throughout 1861 and early 1862, Lincoln was more concerned about holding Kentucky in the Union than freedom for the slaves.
Meanwhile, in his campaign for President in 1932, FDR attacked Hoover from both the left and the right, in the latter case for wasteful deficit spending. It is worth noting that FDR actually imposed an austerity program after his reelection, which triggered the sharp 1937-38 recession.
Given who they were, and not the heroes of memory, would they be considered contenders today?