FDR dying of a heart attack any time in his third term was imminent, congestive heart failure exacerbated by exhaustion, stress, smoking, polio, age, diet, etc.. Thomas Fleming in "The New Dealer's War" found he was lucid and functional often only an hour or two a day by 1943 with noticeably diminishing memory, mental acuity, ability to focus on what he was reading or hearing, etc... Jimmy Byrnes, titularly the Postmaster General, is pretty well the acting President but has no standing to step in with FDR's death (but a concealed disability, he's in the role of Colonel House with Wilson after Wilson's stroke or for us classicists, what Frank Langella's character was doing in the comedy "Dave.") Henry Wallace gets a bad rap. He was a Republican before joining FDR's cabinet, his father had been Secretary of Ag during the Republican administrations in the 1920's and his grandfather a close ally of Theodore Roosevelt. He appeared liberal in the old style of being genuinely interested in most people, from working on Latin American and rural U.S. economic development, curing rickets in the South, and making influential speeches and articles for the common man that are more Four Freedoms than the competing ideologies. He was already pushing creation of the United Nations and had done a lot of the diplomatic work in Latin America, while also having toured Russia (duped there with Potemkin Villages to an unknown extent, fooling a top farming expert about Russian farm collectives' effectiveness would be very difficult. No President before (other than John Quincy Adams who'd been ambassador there) or since had as much knowledge of Russia as Wallace which seems like it'd be kinda handy in the postwar world as well as the race for Berlin.
He'd also been sitting in on the Manhattan Project top team, chasing all of the natural resources inputs for the war effort, etc. so actually better prepared than Truman or Byrnes (political hack) to step in.
Given some time as President (VP from 1940-, Sec. of Ag 1932-1940, Sec of Commerce after VP-that's a pretty distinguished record few have had) I think Wallace would have had a good shot at the 1944 election.
Wendell Wilkie was over. Nothing much to run on left other than China policy and his 2 time campaign manager Albert Lasker from Lord & Thomas Advertising in Chicago had retired in 1942 from most things...and Lasker was a major factor in the credibility of Wilkie's campaigns.
General George Marshall wouldn't run and was still busy running the war as the only Allied leader in the same job from 1939-1945. Eisenhower might well have picked up a cabinet job after the war as his older brother Milton had been Wallace's right hand man at USDA for 8 years and was considered the smarter, more accomplished of the 5 Eisenhower brothers (my aunt's descended from one of them.)
Dewey in 44, maybe and much stronger against Wallace than FDR, but maybe someone else runs on the Republican side (maybe that's MacArthur, pickings for national figures are slim as the minority party for 12 years now in '44.)
Wallace had a very clean private life, J. Edgar Hoover would have lacked leverage there just as he would have with Tom Dewey, and I think either man would have been no-nonsense towards the quite nonsensical Hoover and Wild Bill Donovan, which'd be thousands of butterflies in itself.