The Cheneys are championing a strain of national security conservatism that waned even within their own party because of the flawed intelligence leading to the Iraq invasion in 2003 and the later travails of the occupation. Even Mr. Bush’s brother Jeb Bush has said that if he had been president, he would not have authorized the invasion had he known then what he knows now, a position shared by other Republican candidates.

And yet, the post-Iraq isolationist streak that seemed on the ascendance for a while has also begun to fade with the rise of the Islamic State (also known as ISIS) in Syria and Iraq and Russia’s intervention in Ukraine. Although today’s candidates are not showcasing the unpopular Mr. Cheney in their campaigns, they are, to some extent, voicing a more hawkish message on foreign policy, especially amid the debate over Mr. Obama’s nuclear agreement with Iran.

Whether Mr. Cheney is the right messenger for the moment is open to question. While even some Democrats agree with his criticisms of Mr. Obama — that he has given away too much to Iran, that he has not done enough to help Ukraine against Russia, that his withdrawal from Iraq paved the way for the Islamic State — Mr. Cheney all but invites the “well, what-about-you” counterargument.

Mr. Cheney accuses Mr. Obama of misstating intelligence and lying to the American people about the terrorist attack in Benghazi, Libya, just as his own critics accused him of doing about Iraq’s unconventional weapons. He criticizes Mr. Obama for premature declarations of near-victory over Al Qaeda, just as his own critics accused him of premature declarations of near-victory in Iraq during the worst of the war in 2005 and 2006.

Image Dick Cheney and his daughter Liz wrote “Exceptional,” a stinging indictment of President Obama and his foreign policy. Credit... David Kennerly/Getty Images

Mr. Cheney himself sees a more fundamental difference with Mr. Obama, embracing the argument that the president does not believe in American exceptionalism. “The touchstone of his ideology — that America is to blame, and her power must be restrained — requires a willful blindness about what America has done in the world,” the Cheneys write. “It is fundamentally counterfactual. When President Obama’s ideology has come crashing up against reality, America’s security has suffered.”