He opens with some foreshadowing: "I am happy to join with you today in what will go down in history as the greatest demonstration for freedom in the history of our nation." He is telling the ruling class in America at that time that he's about to open a rhetorical can of worms. And so he does.
Since his primary audience was the very people who held in their hands the power to reform current policy, Mr. King begins a long series of appeals to them. He begins with an allusion to Abraham Lincoln, both directly and indirectly. He uses "Five score years ago" and later "hallowed spot" to correlate with the Gettysburg Address. This appeal incorporates almost his entire audience. Abe Lincoln was championed by the African-Americans for obvious reasons, but he is and was also held in high regard by most white people who had affectionately referred to him as "Honest Abe". In 1963 the only people who might have felt that Abraham Lincoln did not deserve accolades would have been a small minority of whites who disagreed with the Emancipation Proclamation. Although racism was rampant in the 1960's, I doubt that the majority of whites then in the south really wanted slavery to have continued. Mr. King pulls out a few tricks to bring many of them on board as well. One of these was to use "manacles" and "chains" to remind the white population of the slavery they had inflicted upon his people.
I think one of Martin Luther King, Jr.'s best tactics was the allegory of an unpaid check. During a period in America where men did business on their word and a handshake, his allusion to the promise of freedom for slaves being defaulted upon probably made an impact on the conscience of many people. Putting it in terms of an unpaid debt made many people re-think their position on what should have been a clear premise in the 1860's.
Mr. King also does a good job of appealing to the patriots of the American ideal of freedom in these sections:
When the architects of our republic wrote the magnificent words of the Constitution and the Declaration of Independence, they were signing a promissory note to which every American was to fall heir. This note was a promise that all men, yes, black men as well as white men, would be guaranteed the "unalienable Rights" of "Life, Liberty and the pursuit of Happiness".No self-respecting patriot in the USA would disparage these clauses from the US Constitution and the Declaration of Independence. King's passage of rhetoric also solidifies the guilt in those who believed in a moral obligation to pay one's debts.
And,
I have a dream that one day this nation will rise up and live out the true meaning of its creed: "We hold these truths to be self-evident, that all men are created equal".
Martin Luther King, Jr. definitely threw into his speech a lot of biblical reference. This afforded him some leverage with those of all races who valued the Bible. "[T]he dark and desolate valley of segregation...", "the valley of despair", and "...every valley shall be exalted" are probably all akin to Psalms 23:4. He quotes portions of Isaiah 40: 4-5 in concluding his "I have a dream" repetitions with, "I have a dream that one day every valley shall be exalted, and every hill and mountain shall be made low, the rough places will be made plain, and the crooked places will be made straight; "and the glory of the Lord shall be revealed and all flesh shall see it together." He refers to Daniel 2:45 when he says, "With this faith, we will be able to hew out of the mountain of despair a stone of hope". The statement, "Now is the time to lift our nation from the quicksands of racial injustice to the solid rock of brotherhood. Now is the time to make justice a reality for all of God's children" is in reference to Matthew 7:24-27.
In a couple of places in his speech, Mr. King indicates a pretty specific audience. He is direct and critical of Alabama and Mississippi especially. He mentions some other states but this sentence, "I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression, will be transformed into an oasis of freedom and justice" vilifies Mississippi, with "even" being the operative word. He rebukes the "vicious racists" of Alabama and directly reproves their governor "with... his lips dripping with the words of "interposition" and "nullification."
I think Mr. King even attempted to appeal to those entangled in the arising drug culture. "This is no time to engage in the luxury of cooling off or to take the tranquilizing drug of gradualism" was most likely said to spark their interest. He makes no criticism of taking drugs, per se, only a criticism of taking the "drug of gradualism" in regards to his cause.
Mr. King directly addresses the African-American component of his audience further along in his speech. He redirects the speech at one point saying, "But there is something that I must say to my people". He then proceeds to appeal to both those who are feeling more hostile and those who are more passive. This is evident when he describes the movement among African-Americans this way: "[a] marvelous new militancy which has engulfed the Negro community..." Calling militancy "marvelous" lets those who are feeling hostile know that he does not condemn their feelings, yet he proceeds to promote peace. This is an effectively ambivalent statement.
King does not fail to acknowledge the struggles of his people and to put himself on par with them. At one point, he speaks to those who have been in jail. He describes their cells as "narrow", demonstrating his own experiences with being unjustly imprisoned. He continued to elucidate his understanding of his people's persecutions, calling their plight "redemptive".
Possibly, King's greatest appeal to the African-American portion of his audience was his use of phrases from the negro spiritual "Free at last! Free at last! Thank God Almighty, we are free at last!" Prior to this powerful conclusion he makes a final appeal that attempts to unify his entire audience, "that day when all of God's children, black men and white men, Jews and Gentiles, Protestants and Catholics, will be able to join hands..."
This is just a thought, but I find it interesting that there is no reference in the "I have a dream" speech to people of Native American, Latino, or Asian heritage. These ethnic groups also had a pretty rough time in America throughout its history but there is no appeal to them as an audience. Nor is their any appeal to various religions other than those based on the Bible- no appeals to Buddhism, Islam or other prominent non-Judeao-Christian beliefs. Although Mr. King's rhetoric achieved widespread fame and recognition, I think it would have helped his cause even more to verbally reference these various groups rather than just leaving it to implication.