The title of course comes ultimately from the section of the US constitution outlining the powers of the Senate as a check on an over-weening president. (I am sure that this consideration is going to be much discussed by the experts on both sides of the Atlantic in the months to come in view of the 2016 election result.) The phrase is used in particular of presidential appointments which must be made with the "advice and consent" of the Senate. The verb "advise" is what appears in the Senate rule book.
I do not know the book, but was impressed by the film. Like many interested in politics at the time, this first detailed exploration on screen of the working of the American system fascinated me. It seems that like many iconic movies, it was based on a poorly-written book. The ponderousness of the film which I put down to Preminger's heavy-handed direction was, it seems, inherent in the novel.
Mr Teachout highlights how quickly the book fell from the public consciousness (so much so that the Liberal Democrats' super-wonk Mark Pack had not heard of it in 2014*.) but also how it has been taken up again by a new generation of political groupies.
Mr Teachout's key point is that we are no longer in a period when any shame would cause a prominent politician to commit suicide, even in the conservative United States.
Maybe the point on which the plot turns has lost its power, but the political fundamentals are the same. The film may be long, but I advise seeking it out. An incidental pleasure is enjoying the late flowering of such stars of Hollywood's golden age as Lew Ayres, Charles Laughton, Walter Pidgeon and Gene Tierney.
* See the notes to this article. Incidentally, "Fail-Safe" has been returned to late-night TV viewing, I am glad to say. Dr Pack had heard of another key political thriller, Gore Vidal's "The Best Man". I would recommend this work also.