Metal Gear Solid: Peace Walker is about this idea. Set during the Cold War, the theory is that no human will choose nuclear retaliation if attacked, since it means mutual annihilation. However, American nuclear doctrine at the time assumes the threat of retaliation is the only thing deterring an attack. They attempt to solve this by building an AI which will retaliate, but are baffled when it too refuses to return fire.
Present day hair trigger dead hand switch to release retaliatory nuclear strike is very likely on alert levels comparable to period 1982 - 1991, when the Cold War died.