It is very unlikely there would have been a second American civil war in the 20th century. There were no ongoing constitutional crises (over slavery) which caused the Civil War. Nor was the democratic process ever challenged or lost legitimacy. One of the good things about a well functioning democracy is that no one person is essential. Consensus builds and there is a deep bench to draw from. For a civil war to happen, both sides need access to a lot of guns and willing recruits, and ultimately the US didn't have any significant group that was going to challenge the Federal government.
There was a lot of continuity between Hoover and FDR in terms of their approach to the Depression so FDR wasn't absolutely essential to his programs being enacted. There was a lot of consensus being built. In fact, a lot of the things FDR gets credit for actually began under Hoover. Even the Bank Holiday was originally a Hoover proposition, it's just that Hoover wanted to announce it with FDR in order to garner the most public support for the measure, but FDR wouldn't agree to announce it together. Most of the good things that came out of the New Deal was likely to happen even without FDR. The things that were likely to have been unique with FDR are probably those elements that are the most controversial in terms of their impact, or things that we know didn't work like the NRA or the Court Packing scheme. If FDR isn't around, then other people will likely step up.
The closest public disturbances in the US occurred in the late sixties and early seventies. That is the most likely time for some kind of uprising, but again there are long term factors that prevented it from exploding. Progress in civil rights was being made (indeed, the major improvements had already been made before the late sixties) and the Vietnam War was ending. Even a series of blunders or mistakes at this time was unlikely to divide the country into armed camps, although domestic terrorism could have become worse as groups like the Weather Underground became as successful as the Red Brigades or Red Army Faction in Europe.