All in all, apart from the creditable record they earned in World War II, the children of Franklin and Eleanor Roosevelt cannot be considered to have been great successes. In their personal lives, there was divorce after divorce. Their business careers were dogged by charges that they were trafficking on their family name, and by other ethical problems as well. In their political careers, none of them achieved success remotely comparable to their father's. Perhaps it is not reasonable to expect them to have done so.
Still, there was a time great things were expected of them. Two years after FDR's death, Arthur Schlesinger, Jr., observed: "The Roosevelt family is obviously not a spent force in American political life. In 10 years - maybe sooner - two of the most important states might have Roosevelts as governors..." It was not to be, but it is arguable that this was at least partly a matter of bad luck. James Roosevelt had the misfortune in 1950 to be up against California Governor Earl Warren at the height of the latter's popularity (Warren carried every county in the state!). Eventually, Jimmy became Congressman from a safe Democratic district in Los Angeles, and then US ambassador to UNESCO (his mother's old job).
As for FDR, Jr., in 1949 he seemed the next man to watch in American politics. As candidate of the Liberal Party he trounced a Tammany Democrat to win a Manhattan Congressional seat. He was spoken of as the next governor of New York, and perhaps even as a president. But his record in Congress was disillusioning to some of his liberal followers. He voted a "correct" labor-liberal line, to be sure, but he was often slipshod on his homework and absent when needed. In 1954, hoping to become the Democratic candidate for governor of New York, he tried to change his image. He gathered a team of skilled brain trusters, and set about to master the issues. He was considered likely to win the nomination--but the party decided on Averell Harriman instead, who narrowly won the general election. As a consolation prize, FDR, Jr. got the party nomination for state Attorney General. Unfortunately, just like Jimmy in California in 1950, he had to run aginst a very popular liberal Republican--in his case, Jacob Javits. Javits won easily.
After this, FDR, Jr.'s career was, to put it kindly, spotty. He became a Washington-based distributor for Fiat automobiles and a registered agent for Dominican dictator Trujillo. Campaigning for JFK in West Virginia in the 1960 presidential primary, he wondered out loud where Hubert Humphrey had been in World War II--which was pretty generally condemned as a low blow (by among others, mother Eleanor who was backing Humphrey). When JFK named him Under Secretary of Commerce, there were howls of protest from both Left and Right. (A Herblock cartoon pictured Franklin, Jr. sitting on a pile of Trujillo money, and saying "I am broadminded--I am just as willing to work for a democracy.") He later became the first chairman of the newly created Equal Employment Opportunity Commission, and in 1966 was Liberal Party candidate for governor of New York. The Liberals chose him, not out of any conviction that he was a liberal but in the cynical belief that only his name would allow them to remain the third party in New York, ahead of the new and rapidly growing Conservatives. As it turned out, though, Franklin, Jr. finished fourth, behind not only the Republican and Democratic candidates but (just barely) behind a little-known Conservative as well. He was to live until the age of 74 (in 1988) but his political career was over.
So what's the PoD for making Franklin, Jr. a political success--indeed, maybe even getting him into the White House? No less a political expert than John F. Kennedy "thought that if Franklin Roosevelt, Jr., had only secured the support of Tammany boss De Sapio in 1954, he would have become the Democratic gubernatorial candidate, he would have won, and he would have been the 1960 presidential nominee." "The Roosevelt Dynasty" article written by Stephen Hess in "America's Political Dynasties", Doubleday & Company, Inc., NY, 1966; the section discussing FDR, Jr. is at
https://web.archive.org/web/2005050...rg/forums/viewmessages.cfm?Forum=41&Topic=111 (Hess' article is my chief source of information on FDR, Jr.) Even if he would not be nominated as president in 1960, I could easily see him being nominated as vice-president--but *not* if the ticket were headed by JFK (two Northeasterners being an unlikely ticket). I could certainly see LBJ-Roosevelt or Symington-Roosevelt (if, say, JFK had died during back surgery or had been defeated by Lodge in 1952 or had been vice-presidential nominee in 1956 and was widely blamed for the ticket's poor showing). And of course once he becomes vice-president, we just have LBJ or Symington visit Dallas in 1963...
But all this assumes a number of things: First, that if Franklin, Jr. got the Democratic nomination for governor in 1954, he would win. This is at least possible, but given that Harriman's victory was narrow, far from certain. Second, that he be re-elected in 1958. Even if he does a good job as governor, this will be a problem, because (a) the New York Democrats were having terrible factional disputes between "regulars" and "reformers" and (b) the GOP had a most attractive candidate in Nelson Rockefeller. Of course one reason for the Democrats' factional disputes may have been that Eleanor Roosevelt was angry with Tammany for not backing her son for governor in 1954 but even if Eleanor got along better with De Sapio, there would still be regular-vs.-reformer tension. In any event it is at least conceivable that FDR, Jr. would be less inept politically than Harriman was as governor and so might have a better chance in 1958, even against Rockefeller (indeed, maybe Rockefeller will even decide not to run, thinking that a Roosevelt is going to br a lot more popular with the average New Yorker than a Rockefeller).
An FDR, Jr. presidential or vice-presidential candidacy might run into some "birtherism" since he was born at Campobello Island, New Brunswick.
https://en.wikipedia.org/wiki/Franklin_Delano_Roosevelt,_Jr. However, I do not think that this will be a serious factor; at most, it would be an excuse for those who didn't want to vote for him anyway. The prevailing view among lawyers, then as now, is that those born to American citizens temporarily living abroad are "natural born citizens" within the meaning of the Constitution.