In the "great silent majority" speech in November of his first year in office, Richard Nixon appealed to the majority of Americans who he claimed were behind his policy in the Vietnam War over the heads of the hundreds of thousands of anti-war Americans who were at various times out in the streets being very vociferously against his policy. Taken on this level, the speech came to represent an elected government sticking to its guns (quite literally) in the face of a loud minority. The speech achieved what politicians always dream speeches will achieve but what they almost never do, especially in the internet age: it managed, for a while, to redefine the national conversation and buy the government more time for its policies. But its real genius consisted in something else.
Since getting into power, Nixon had pursued a plan to end the Vietnam War which consisted of diplomatic offers and escalations of force. This was when he first bombed Cambodia, hitting North Vietnamese supply lines and storage dumps in an effort to force them to make concessions at the bargaining table. But, as Nixon said in his speech, all that had been achieved in the negotiations so far that year was a decision over the shape of the table that the negotiations were to take place around. The negotiations wouldn't go anywhere because the two sides had radically incompatible demands - the Communists wanted the U.S. to withdraw from South Vietnam and overthrow the South Vietnamese government, its ally, on the way out. America refused, and Nixon plotted even more dramatic escalations of force against the North to force them to back down from their demands.
A secret plan to brutalize North Vietnam was put together, and it was called Duck Hook. No option was considered off the table in the plan, which would definitely involve resuming the bombing of North Vietnam with B-52s - something that had stopped after the Tet offensive - and putting naval mines around North Vietnamese ports to stop supplies getting in, a step that had been rejected in the past because of the risk of damaging Soviet or Chinese vessels and widening the war. Henry Kissinger was all in favour of the plan, and he had his staff draft it, and Nixon was carried along by the idea for a while - he liked the idea of being tough, taking shocking actions, and appearing unpredictable to his enemy. The speech on November 3rd - the speech that eventually became the one about the "great silent majority" - was initially pencilled in to be the speech that announced the beginning of Duck Hook.
Then Nixon changed his mind. Early November was the most important part of the calendar for the antiwar movement that year, with demonstrations planned all over the country. Nixon had little respect for the antiwar movement, but he did respect their ability to create a political problem for him, and he knew that if he launched a savage attack on North Vietnam just as the streets were filled with protesters, he would become their biggest target. He also knew that his threats of further strikes against North Vietnam would look much less credible when his own policy was so demonstrably unpopular at home. Nor did he any longer believe that the chances of scaring North Vietnam into compliance with his diplomatic terms were good: the coercive strategy, the strategy of hawks, wasn't going to work.
And so the speech that was about a government following the path it thought was right, with the silent support of good citizens and in defiance of a vocal minority on the streets, only came about precisely because of that vocal minority - Nixon was doing the opposite of what he claimed he was doing in his wildly popular speech. This was partly because even though he was claiming the support of the "majority", Nixon - facing both George Wallace and Hubert Humphrey - had not even won a majority of the votes cast in the 1968 presidential election, and was nervous about his popularity. Realizing the domestic base for his policy of coercion didn't exist, he reversed himself and then made the speech the start of a new PR campaign to win back support for his policies and try to blunt the growing power of the antiwar movement. But the movement had won a great victory, perhaps without even knowing it. And that story tells you a lot about the power of protest when it is deep-seated enough in society and about the political adaptability, disingenuousness, and genius of Richard M. Nixon.