Can you clarify, specifically, which iteration of a Nazi, or fascist party you are asking about?
EDIT: OP has clarified.
So, the German American National Socialist movement in the US is very interesting, and it took several different forms before the German-American Bund became what it was, but if we're speaking specifically about the Bund and not any of it's predecessor organizations, then we could probably point to the 1936 Summer Olympics as the zenith and nadir of the German-American National Socialist movement. Bundführer Fritz Kuhn had met and had his picture taken with Adolf Hitler, and presented Hitler with a "golden book" that was a history of the Bund in the United States. Allegedly, Hitler thanked Kuhn for the book and told him to "Go over there and continue the fight."
While Kuhn and the Bundists celebrated this as an official endorsement - it wasn't, and it was a public relations disaster for Germany. They had struggled time and again throughout the 30s to try and close the lid on the Bund and its predecessor organizations. In October of 1935, they had cut off funding to the "Friends of New Germany" and in December of 1935 Rudolf Hess had ordered all German Nationals out of the group. It dissolved in 1936 and was replaced by Kuhn (a naturalized American) and the German American Bund.
Although the German government had recognized the photograph of Kuhn and Hitler to be an immediate disaster (Kuhn was never allowed so close to Hitler again), Kuhn and the Bundists would not realize that the photograph would be their undoing until 1937, as federal officials began to investigate the activities of the Bund (first the McCormack-Dickstein Committee, and later the Dies Committee). As a result of increased scrutiny and investigations, the Bund lost 13% of its membership in 1937 and newspaper advertising revenues (one of the primary ways that the Bund was funded, dwindled).
Kristallnacht in November of 1938 created an international uproar, and the United States was no exception. The German government, Hitler, and National Socialism were deeply unpopular, particularly in the American press. The German state was equated with a slave-state, and Hitler's sanity were frequently called into question. The Bundists had constantly and consistently over-exaggerated their ties to a now increasingly unpopular German government.
The German American Bund's "Pro-American rally" at Madison Square Garden on February 20, 1939 was a desperate attempt for publicity from an organization already in steady decline. Seeking to convince Americans of their alignment to American core values and history, the rally was held to celebrate George Washington and attempted to depict the first American President as the first fascist. Bundist speakers drew connections between the leadership of Hitler and that of Washington, and called for cooperation between all American fascist and national socialist organizations.
As a result of the above-mentioned increased scrutiny, the German American Bund was audited by the state of New York, and dissatisfied with the Bund's response, their offices were raided in May of 1939. Kuhn was charged and convicted with embezzling $14000 dollars from the organization, and was expelled from the organization in December of that year. The Bund, which had declared "Kuhn is the Bund" never really recovered from this, though it did continue to exist. The group held a national convention in Chicago in August of 1941, and in 1943, many of the naturalized members of the group were de-naturalized. Kuhn himeslf was deported to Germany after the war.