How we cite our quotes: (Paragraph.Sentence)
Quote #1
Let us all understand that the question before us is not whether some Americans are for peace and some Americans are against peace. (19.1)
Think about this in terms of delicious pizza. Everybody loves pizza—this much we can agree on. Nixon is just saying that those protesters who don't support his policies in Vietnam are the pizza weirdos: the ones who put anchovies, pineapple, and probably grape salad all over their pizzas.
Quote #2
Well, one of the strengths of our free society is that any American has a right to reach that conclusion and to advocate that point of view. But as President of the United States, I would be untrue to my oath of office if I allowed the policy of this Nation to be dictated by the minority who hold that point of view and who try to impose it on the Nation by mounting demonstrations in the street. (116.1-116.2)
Here's the meat and potatoes of Nixon's whole argument. Nixon really didn't want all those anti-war protestors to change the events in Vietnam. So, he's saying that they're just a small fraction of Americans, and therefore shouldn't really have that strong a voice in politics, especially in regard to the war in Vietnam.
Quote #3
If a vocal minority, however fervent its cause, prevails over reason and the will of the majority, this nation has no future as a free society. (117.2)
If the previous statement represented Nixon's meat and potatoes, this one is the side salad with a healthy dollop of contempt for dressing. Nixon really didn't want those anti-war protestors to change the events in Vietnam, so here he's basically saying that if the anti-war protestors get their way, the United States would crumble, and war would probably break out anyway.
Quote #4
Let historians not record that when America was the most powerful nation in the world we passed on the other side of the road and allowed the last hopes for peace and freedom of millions of people to be suffocated by the forces of totalitarianism.
And so tonight—to you, the great silent majority of my fellow Americans—I ask for your support. (130.1-131.1)
The food metaphors continue: this was Nixon's cherry, sitting atop his speech-giving ice cream sundae. He's calling on all of his supporters to join him and enjoy the delicious rhetorical meal that he has created for them—all in return for helping to get his plans for Vietnam passed. And America ate it up. (Pun intended.)
But Nixon didn't want to invite the anti-war and hippie crowds to join in. He assumed that they don't like ice cream…it's not vegan.
Quote #5
Let us be united for peace. Let us also be united against defeat. Because let us understand: North Vietnam cannot defeat or humiliate the United States. Only Americans can do that. (134.1-134.4)
Nixon just couldn't leave it at the speech's peak moment. He really hit a high mark with his reference to the "great silent majority," but he had to have the last word on the anti-war crowd. This little jab is meant to get those protestors to feel super bad for not being pro-Nixon supporters.