In his famous "I Have a Dream" speech, Martin Luther King is actually a bit vague as to what he means when he warns America "will have a rude awakening" if Americans fail to see the urgent need for change and return to their everyday, segregated, racist affairs because they believe African Americans will back down after venting a little frustration. He is, however, very clear on what he believes the "rude awakening" should not be.
In a later paragraph, he speaks out against the "militancy," or violence being promoted by the Black Power Movement of the 1950s and 60s. Instead, as a staunch advocate of peaceful protest, King supports protests in the forms of boycotts, demonstrations, sit-ins, and marches. We know the "rude awakening" lead by King would continue in these forms because he gives his people the following warning:
In the process of gaining our rightful place, we must not be guilty of wrongful deeds.
He further warns, "We must not allow our creative protest to degenerate into physical violence." His use of the phrase "creative protest" implies that he will continue to promote peaceful means of protest, even in the face of giving the nation a "rude awakening."
While we are not told specifically what to expect of such an awakening, we are told what triumphs he expects such an awakening to bring. He expects true equality to be acknowledged, true freedom, true justice, brotherhood among whites and blacks, an end to oppression, an end to discrimination, and an end to segregation.