What kind of struggle for equal rights does Dr. Martin Luther King, Jr. visualize?

Dr. King envisioned a difficult struggle for equality because its path was through nonviolent civil disobedience.
The struggle that Dr. King envisioned for equal rights was a complex one.  He made this understanding a cornerstone of his speeches, writings, and actions.  Dr. King knew that the Civil Rights Movement would not be successful unless it was seen as more than a political exercise.  He had to broaden its appeal so that white Americans could see inequality as a moral reality that had to be stopped. Embracing nonviolent civil disobedience was the only way he could move the fight for equality from a political to a moral reality.
Events like the Montgomery Bus Boycott demonstrated how Dr. King envisioned the difficult struggle for equality. He encouraged his followers to not take buses in order to protest segregation in the Montgomery public transit system.  African-Americans who depended on buses to get to work had to make other arrangements.  Sometimes, this involved walking long distances.  However, Dr. King stressed that the boycott would emphasize how African-Americans would not passively accept the injustice of segregation.
As a result of such advocacy, Dr. King and his followers experienced much difficulty and resistance from Southern whites. This included harassment and violence.  When Dr. King's house was firebombed, the words he spoke to followers revealed the difficulty of the path towards equality:  

If you have weapons, take them home; if you do not have them, please do not seek to get them. We cannot solve this problem through retaliatory violence. We must meet violence with nonviolence. Remember the words of Jesus: 'He who lives by the sword will perish by the sword.' We must love our white brothers, no matter what they do to us. We must make them know that we love them. Jesus still cries out in words that echo across the centuries: 'Love your enemies; bless them that curse you; pray for them that despitefully use you.' This is what we must live by. We must meet hate with love. Remember, if I am stopped, this movement will not stop, because God is with the movement.

Through his appeals to nonviolent civil disobedience, Dr. King showed how the struggle for equality involved making the Civil Rights Movement an ethical issue instead of a political one. This was a very challenging pivot to make. However, people began to recognize that Dr. King was appealing to moral issues and not merely legislative ones.  The Montgomery Bus Boycott was one of the first moments where Dr. King showed his vision for racial equality.  He knew that its complex path would go through nonviolent civil disobedience, transforming what used to be seen as a political issue into a moral and spiritual call to action.