Part of Nixon's foreign policy was to try and trick 2nd world countries into believing that Nixon was a "madman" and that he may react irrationally to provocation. It seems like that would be a hard sell if at the same time he's reassuring American citizens that he wouldn't trigger a nuclear war. How was Nixon able to appear calm and rational to American while appearing terrifyingly irrational to our enemies?
Nixon never campaigned on "Madman Theory," nor is it clear he ever totally acted upon it. There are very few examples of this "strategy" in practice. It is more something Nixon talked about with his advisers than anything that guided his policy, and it was definitely not something he talked about publicly. The idea of "Madman Theory" did not become public until 1978, when his former chief of staff H.R. Haldeman wrote a tell-all memoir, The Ends of Power, and discussed it.
After Nixon's presidency, there were a lot of public discussions about this sort of thing, and his drinking, and the dangers in having him in charge of the "button." It was, in fact, one of the few public discussions of this issue that has been had (the only Congressional hearings on this subject are directly related to this), until the most recent election. (At some point I will finish my piece on nuclear themes in Presidential elections — it is a work in progress.)
Nixon's public face on nuclear issues was as someone who supported arms control initiatives, by contrast. He signed the Nuclear Non-Proliferation Treaty, the Anti-Ballistic Missile Treaty, and unilaterally ended US biological and chemical weapons research. In retrospect, this was in part because he didn't believe treaties were all that important, not how the world really "worked." But that only came out years afterwards.
I elaborate a bit more on Nixon and the bomb here, citing the really quite interesting book Nuclear Statecraft by Francis Gavin, which gives a lot of careful study to these matters.