The time was ripe for the Civil Rights Movement for two major reasons. First, the Supreme Court came out decisively on the side of equal rights. Secondly, blacks in the US had advanced economically in large enough numbers that their buying power and therefore their boycott power were enough to advance the cause and change some reluctant white minds.
Martin Luther King Jr.'s role, in my opinion was that he did not make the revolution, but he accelerated it. He was so magnetic, eloquent, respected and focused that he helped speed the change along.
Martin Luther King, Jr. had many great qualities. He was a great leader, speaker, organizer, very passionate, etc. I do not think he made The Movement but I do think he had a great deal to do with its success.
Martin Luther King, Jr. advocated non-violence and peacefulness. I think this is very important because if he had not done so many of the protests, sit ins, marches, etc. may have been violent. This could have destroyed everything. Violence is not the message he wanted to get out, rather he wanted the issues of equally brought out into the open. He was very successful in doing this.
This is a fairly interesting question and one that has some fascinating implications. The larger issue at stake here is if individuals are strong enough to mold events in accordance to their own subjectivity, or if individuals are part of a larger social consciousness that transcends individual components. Like most questions of this nature, the answer is complex. There are many elements that would suggest that King was uniquely qualified to carry the torch of social change that the Civil Rights Movement demanded. With his stress on civil disobedience and nonviolent calls to dissenting action, King was able to galvanize support all over the country, from different narratives. At the same time, King was a leader that did embrace the broader narrative of the time period that was able to articulate a vision of how reality could be as opposed to what is. Both of these polarities of being part of a movement and leading it would be apt descriptors of Dr. King and his role during the time period.
I am going to take the easy way out on this and say that it was a little bit of both.
Certainly, the Civil Rights Movement was not exactly made by Dr. King. In many of the major events, he was not the main player or was not really involved at all. The movement was made by the individuals who put themselves on the line to fight for their rights.
However, it seems likely that the movement would have had less success if there had not been a charismatic leader like King. His speaking and writing ability and his personal presence helped put a face on the movement and make it more appealing to many Americans.