Soviet/Communist/Isel in plot was crazy + wouldn't have worked
The Soviet/communist/Iselin plot was crazy and wouldn't have worked even if the brainwashed medal of honor winner, Raymond Shaw had succeeded in assassinating the President of the United States.
The intention of the C.B's (including Raymond's nutjob mother) was that once the President had been assassinated, right wing Republican Vice Presidential candidate (and nutjob) John Iselin would step forward make a rousing speech about how the C.B's and the Soviet Union had been responsible and whip up a frenzy of right wing patriotism that would sweep the right wing Iselin into an overwhelming victory as President.
But look at what happened in real life - a year after this movie was released the President of the United States WAS assassinated and by a 'commie with links to the Soviet Union as well'!!!!!!!!! The public DID NOT then overwhelmingly vote in the very conservative, right wing, anti-communist Barry Goldwater. Quite the opposite, Democrat Lyndon Johnson (with his socialist 'Great Society') was elected President with an overwhelming majority (486 - 52)
Going back to the movie - the American public would have listened to the John Iselin candidate for about 30 seconds, then the vast majority would have thought,
'Who the hell is this nutjob??? Let's vote for Lyndon Johnson instead'
Then they would have gone to the polling booths and cast their votes for 'Landslide Lyndon'.