"The Best Man" from the play by Gore Vidal is on TCM at 10 AM EST tomorrow (Monday). It's one of my favorite films of all time, and so worth a look!
From Wikipedia (I've removed one sentence so not to ruin the film's ending):
http://en.wikipedia.org/wiki/The_Best_Man_(1964_film)
William Russell (Henry Fonda) and Joe Cantwell (Cliff Robertson) are the two leading candidates for the Presidential nomination of an unspecified political party. Both have potentially fatal vulnerabilities. Russell is a principled intellectual (believed by many critics and fans to be based on Adlai Stevenson). A sexual indiscretion has alienated his wife Alice (Margaret Leighton). In addition, he has a past nervous breakdown to live down. Cantwell (likely modelled on Richard Nixon or possibly Joseph McCarthy) portrays himself as a populist "man of the people", but is a ruthless opportunist, willing to go to any lengths to get the nomination. Neither man can stand the other; neither believes his rival qualified to be President.
They clash at the nominating convention and lobby for the crucial support of dying former President Art Hockstader (Lee Tracy) (likely modelled on Harry Truman). The pragmatic Hockstader prefers Russell, but worries about his indecisiveness and overdedication to principle; he despises Cantwell, but appreciates his toughness and willingness to do what it takes.
One of Russell's aides digs up Sheldon Bascomb (Shelley Berman). He served in the military with Cantwell and is willing to expose his homosexuality. Hockstader and Russell's closest advisors press him to grab the opportunity, but he resists. As the first round of voting begins, he arranges to meet Cantwell privately, to let him know that he knows his rival's darkest secret. But though Cantwell doesn't understand what makes his opponent tick, he knows this much - Russell doesn't have the stomach for dirty tactics. In the end, (and here's where I took out part of the sentence so not to spoil the film).