To recycle an old soc.history.what-if post of mine:
***
The big issue is whether relations with the USSR would be better than under Truman. It is certain that wartime unity was already coming under strain before FDR's death. When Stalin characterized the US attempts (in the Berne talks) to induce a surrender of German troops in Italy in March-April 1945 as a plot, concocted with Berlin, to keep Soviet troops out of central Europe, FDR angrily wrote to Stalin that "Frankly I cannot avoid a feeling of bitter resentment toward your informers, whoever they are, for such vile misrepresentations of my actions or those of my trusted subordinates." Herbert Feis, *Churchill-Roosevelt-Stalin: The War They Fought and the Peace They Sought*, p. 593.
https://archive.org/stream/churchillrooseve007330mbp#page/n607/mode/2up
There were also disagreements over the interpretation of the Yalta agreement. It had been agreed at Yalta that the pro-Soviet Polish government (originally the Lublin government, then the Warsaw government) would be broadened to include Poles from the London Government-in-Exile and elsewhere, but the Warsaw government claimed a right to veto any London Poles it found unacceptable, such as Mikolajczyk; FDR denied that the Warsaw government had any right to decide *which* London Poles it would accept. "In his message to Stalin, the President said in sum that as he understood it, the reorganization of the Lublin government was to be done in such a way as to bring into being a new government, in which the members of the Lublin government would play a prominent role. But, he added, any arrangement which resulted in a thinly-disguised continuation of the existing Warsaw regime would be entirely unacceptable and would cause the American people to regard the Yalta agreement as having failed..." Feis, p. 575.
https://archive.org/stream/churchillrooseve007330mbp#page/n589/mode/2up Stalin in turn replied to FDR that "Matters on the Polish question have really reached a dead end." Feis, p. 576.
https://archive.org/stream/churchillrooseve007330mbp#page/n591/mode/2up
Another source of tension is that Stalin said that Molotov could not make it to San Francisco for the founding of the United Nations--he was needed in Moscow. This threw into question the Soviet attachment to the new organization, and certainly seemed to be a snub or at least a form of pressure (after FDR's death, it was found that Molotov could make it to San Francisco after all).
Still another point to remember, though of course policy makers in Washington did not know about it yet: the attack on Earl Browder, the American Communist leader, for "revisionism" had already been prepared by this time. (The attack was nominally by Jacques Duclos in the French Communist *Cahiers du Communisme* but everyone knew that Moscow was behind the attack, especially since Duclos quoted sources to which only the CPSU had access.) It is doubtful that the attack on Browder was the declaration of the Cold War which Browder later claimed it was, but it was an indication that Stalin obviously thought that some western Communist parties had gone too far in accommodating themselves to their governments. If not a declaration of cold war, it was at least a warning sign.
On April 6, FDR informed Churchill that "We must not permit anybody to entertain a false impression that we were afraid. Our Armies will in a very few days be in a position that will permit us to become much 'tougher' than has heretofore appeared advantageous to the war effort." This sounds belligerent, but it has been argued that the message was drafted by Admiral Leahy--who like Averell Harriman was a strong advocate of a tougher policy on Russia--and that FDR may have approved it without giving too much thought to its implications.
https://books.google.com/books?id=LPfwANTbzi0C&pg=PA179
FDR's last message to Churchill has often been quoted and can be used to support either side in the "would relations with the USSR have been better if FDR had lived?" debate:
"I would minimize the general Soviet problem as much as possible because these problems, in one form or another, seem to arise every day, and most of them straighten out, as in the case of the Berne meeting.
"We must be firm, however, and our course thus far is correct." Feis, p. 596.
https://archive.org/stream/churchillrooseve007330mbp#page/n611/mode/2up
There is undoubtedly an optimism here that somehow the problems with Stalin can be worked out. OTOH, there is also the insistence that "we must be firm"--and "the course" which FDR mentions is one of refusing to accept Stalin's interpretation of the Yalta agreement, a course which would lead to conflict unless one side or the other backed down. Thus when Truman in his famous meeting with Molotov shortly after FDR's death denounced the USSR for failing to carry out the Yalta agreement in Poland, he may have used less diplomatic language than FDR would have done, but there was no difference in substance on the policy. (And after all, in a few months the supposedly belligerent Truman *did* recognize a new Polish government, which, notwithstanding the inclusion of Mikolajczyk, *was* pretty much the "thinly-disguised continuation" of the Lublin/Warsaw government that FDR had declared unacceptable.)
FWIW, Robert Dallek (*Franklin D. Roosevelt and American Foreign Policy, 1932-1945*, p. 534) has argued that open confrontation between the US and the USSR might have developed *sooner* if FDR had lived. As Dallek notes, trying to maintain good relations with the USSR was one side of FDR's Soviet policy, but there was another side:
"At the same time, however, he acted to limit the expansion of Russian power in 1945 by refusing to share the secret of the atomic bomb, agreeing to station American troops in southern Germany. endorsing Churchill's arrangements for the Balkans, working for the acquisition of American air and naval bases in the Pacific and the Atlantic, and encouraging the illusion of China as a Great Power with an eye to using her as a political counterweight to the USSR. Mindful that any emphasis on this kind of *Realpolitik* might weaken American public resolve to play an enduring role in world affairs, Roosevelt made these actions the hidden side of his diplomacy. Hence, in the closing days of his life, when he spoke of becoming ''tougher' [with Russia] than has heretofore appeared advantageous to the war effort,' he was not suddenly departing from his conciliatory policy but rather giving emphasis to what had been there all along. Moreover, had he lived, Roosevelt would probably have moved more quickly than Truman to confront the Russians. His greater prestige and reputation as an advocate of Soviet-American friendship would have made it easier for him than for Truman to muster public support for a hard line."
https://books.google.com/books?id=xTKvo-cXv3EC&pg=PA534
That last point really should get more attention. Truman was vulnerable to charges that he was betraying FDR's legacy, and this may have inhibited him from taking stronger action against the Soviet Union, at least in 1945. FDR would have a somewhat freer hand. Of course, even if he lived he would be unlikely to have good health, and it can be argued that this would make a reversal of policy difficult. But as Dallek notes, no "reversal" would be
necessary--just an emphasis on a side of his policy that was already there. Furthermore, people like Leahy and Harriman would be there to urge a tougher policy on him. Left-wing critics of Truman often blame him for listening to their advice, but would FDR, especially if he was in bad health, have resisted their influence any more? FDR's quick approval of Leahy's tough-sounding April 6 message to Churchill may be significant here...
https://groups.google.com/d/msg/soc.history.what-if/FM8LwD_ixaw/io_L64p1TY8J