Just as the 1830's have been called the age of Jackson, it is probably fair to refer to the 1930's, politically at least, as the age of FDR. Franklin Delano Roosevelt was the dominant political presence of the age, serving to reinspire faith in the presidency after Herbert Hoover who was blamed by many for causing the stock market crash and subsequent depression. Roosevelt almost singlehandly forged a new political alliance between the working classes of the Northern cities, the farmers of the West and South (both black and white), and generally every group hurt by the Depression. Roosevelt's policies for recovery, his use of the radio in order to talk directly to the nation in his "fireside chats," and his appeals for the government to remember the "forgotten man" all won him massive support among the people. This support resulted in his winning re-election in 1936 with all but eight electoral votes cast in his favor. Moreover despite the fact that no president had ever run for a third term, Roosevelt's popularity gained him victory in 1940 (and 1944 for that matter). This cover, published in the midst of the 1940 campaign season, show Roosevelt wearing many hats (quite literally) as he attempts to portray himself as a man of the people and as a representative of a number of segments of the population that he hoped would again vote for him in November of that year.
Despite the massive margins of victory which Roosevelt garnered and the general public support he received throughout his presidency, he was far from universally loved. Especially during his second term, many conservatives (including many Southern Democrats who disagreed with his leanings on race) came to view his New Deal policies as unjustified and unconstitutional extensions of the power of the federal government. This growing conservative opposition resulted in Roosevelt being forced to step back with some of his initiatives lest they be defeated. In addition to the political opposition he suffered, Roosevelt came to be passionately hated by upper class Northerners who viewed him as a "traitor to his class" because of his policies and rhetoric. Many went so far as to even refuse to mention Roosevelt's name referring to him only as "that man." Given the target audience of the New Yorker, one suspects that this cover may actually be more a subtle form of mockery then a celebration of FDR's populism.