Years later, Cheney watched an episode of the Showtime series "Homeland" in which such a scenario was part of the plot.
"I was aware of the danger, if you will, that existed, but I found it credible," Cheney tells "60 Minutes" in a segment to be aired Sunday. "Because I know from the experience we had and the necessity for adjusting my own device that it was an accurate portrayal of what was possible."
Cheney and Reiner are promoting a book they co-authored, "Heart: An American Medical Odyssey."
In the "60 Minutes" interview, Reiner says he worried that Cheney couldn't stand the pressure that came on Sept. 11, 2001, the day terrorists attacked the U.S. Medical tests seen that morning showed Cheney had elevated levels of potassium in his blood, a condition called hyperkalemia, which could lead to abnormal heart rhythms and cardiac arrest.
Reiner says he watched news coverage of the day's events on television and thought, "Oh, great, the vice president is going to die tonight from hyperkalemia."
Cheney underwent numerous heart-related procedures over the years, including angioplasties, catheterizations and a quadruple bypass operation. However, he says the health problems never affected his job performance during his eight years as vice president in George W. Bush's administration.
Asked on "60 Minutes" if worried about his physical health impacting his judgment and cognition, Cheney replies, "No." He says he was aware of potential side effects from limited blood flow to the brain and effects on cognition and judgment but didn't worry about it.
"You know, I was as good as I could be, you know," Cheney says, "given the fact I was 60-some years old at that point and a heart patient."
Cheney also dismisses stress as having had an impact on his heart disease. "I simply don't buy the notion that it contributed to my heart disease," he says. "I always did what I needed to do in order to deal with the health crisis in the moment."