There was a significant claim of a coup attempt in the 1930s. Smedly Butler, a Marine Corps general and at that time the most highly decorated soldier in US history, claimed to congress that he had been approached to aide in a coup to oust FDR. Long story made short, business leaders were unhappy with the new deal and wanted a change, however they knew Americans wouldn't take the end of republican-democracy sitting down. They planned to get enough support from powerful interests to force FDR into submission. The president would then have to appoint a new cabinet level position who would hold power while the president served out his term as a figurehead.

Whether it was "near successful" is a story for a better historian than I. Sorry about the short post on such an interesting topic I got to go to work.

The first thing that comes to mind are the allegations made by General Smedley Butler that he was approached by a group of businessmen who wished to hire him to lead a fascist coup against FDR in 1934.

Butler was a popular figure with the bonus army that had been disbanded by Hoover in 1932, and Butler alleged that the people who hired him wished to forge this group of veterans into a fascist organisation. During the McCormack–Dickstein Committee hearings, butler's testimony was found to be credible.

The plot to seize the white house, J. Archer, 1973