She recalled that her closest moments with her husband came during the Cuban Missile Crisis in 1962, when the US and Soviet Union seemed on the brink of nuclear war.
Some officials had sent their wives away, but the first lady resisted.
"If anything happens, we're all going to stay right here with you," she remembers telling her husband.
"Even if there's not room in the bomb shelter in the White House. I just want to be with you, and I want to die with you, and the children do, too - than live without you."
She also has harsh words for many other politicians and leaders:
"Jack said it to me sometimes. He said, 'Oh, God, can you ever imagine what would happen to the country if Lyndon were president?"' she said.
She also strongly criticised Dr King, recalling how her brother-in-law, US Attorney General Robert Kennedy, told her the civil rights leader had been intoxicated at JFK's funeral and mocked Cardinal Richard Cushing's Mass.
She said: "He made fun of Cardinal Cushing and [Robert] said that he was drunk at it. I can't see a picture of Martin Luther King without thinking, that man's terrible."
She reserved sharp criticism for world leaders, too.
French President Charles de Gaulle was "that egomaniac" and "that spiteful man", while future Indian Prime Minister Indira Gandhi was a "bitter, kind of pushy, horrible woman".I heard some of the tapes on the news tonight and I thought that was really neat to hear it in her own voices, so I found a news segment for you as well.