I recently listened to Dan Carlin's Hardcore History episode about nuclear weapons. In it, he mentions that Nixon once said this during the Watergate Scandal:
"I could leave this room, and in 25 minutes, 70 million people would be dead."
What is the context of this quote? Could a President give the order to unleash nuclear weapons even if there was no threat to the United States? What if a President is not in his right mind?
The context of the quote was a meeting Nixon had with two members of the House of Representatives (Rep. Charles Rose, R-NC, and Rep. Clem McSpadden, D-OK) in the summer of 1974. The context was apparently Nixon trying to impress upon them that Watergate was a "little burglary" and not that important or worth the fuss, compared to his other responsibilities. Rose remembered Nixon as saying: "I can go into my office and pick up the telephone and in 25 minutes, millions of people will be dead." McSpadden remembered it as "I can pick up the phone and 70 million Russians can be killed in 20 minutes." A third version of the quote was disseminated by Sen. Alan Cranston (D-CA), who was not there at the time but told about it by McSpadden and Rose, was "At any money, I could go into the other room and press a button and 20 minutes later 60 million people would be dead." (It is perhaps worth noting that there is no "button," and the phone call parts ring more true.)
The story got widely circulated in February 1976, along with other discussions of Nixon's final days in the White House. You can read some of the press accounts here.
As for whether a President could give that order, yes. There is nothing that stops a President from ordering the first use of nuclear weapons. The harder question is, are there checks in place whereby other people in the chain of command (the Secretary of Defense, the military generals who enforce such orders) could refuse to do it? I have written on this twice on my blog, and the latter also links to an editorial I wrote for the Washington Post on this question. I have not found any positive evidence which suggests that the Presidential order could be vetoed, and I have heard (again, though, without evidence) from people who know more than a little on this subject that the Secretary of Defense is a by-passable aspect of the chain in this instance. But there is much murkiness on this topic for somewhat obvious reasons. I explain more about this in the second blog post.
As for the issue of determining that a President is not capable of governing, this is covered by the procedures of the 25th Amendment, Section 4. I would only note that it requires a lot of agreement on the subject, and is not meant to be something easy to do. I am (as I note in my post) dubious about it being an effective means to restrain a President's nuclear command authority.