Three challenges Martin Luther King Jr. faced in the battle for equal rights included the opposition of "good" white people to his tactics, his realization that the only way to win civil rights was to proceed nonviolently, and pushback against his plan in the late 1960s to unite Black people and white people in a war on poverty.
King pushed back against critics of his methods. In Birmingham, he led Black people in protest marches and boycotts against racial segregation in that city. After he was jailed for his activities, he learned that a group of eight white clergymen had sent a letter to the newspapers saying he had gone too far. King knew he had to stop this dissent from people who were supposed to be on his side, so he sent his "Letter from Birmingham City Jail" explaining that nothing would be accomplished without disruptive, but nonviolent, action.
King also had the problem of needing white support to get civil rights legislation passed in the United States, because the country was predominantly white and white people held most of the power. He realized that any whiff of Black violence would provide the pretext for white people to crush his movement. Therefore, he trained his followers in Gandhi's techniques of nonviolence and was continually challenged to find ways to protest that were disruptive without spilling over into violence. His nonviolent approach was controversial but ultimately effective.
Finally, King faced opposition when, in the late 1960s, he tried to unify poor Black people and poor white people together in solidarity and spoke out to oppose the Vietnam War. In the end, his message was more than some could take, and he was assassinated in 1968.
Martin Luther King, Jr. was a leader of the Civil Rights movement who faced enormous challenges in his lifetime. His first major protest was the Montgomery, Alabama, bus boycott of 1955-1956, when he, along with Rosa Parks, protested conditions that African-Americans faced on buses in that city. Under the laws of Jim Crow, African-Americans were forced to move to the back of the bus in Montgomery and other southern cities when whites boarded, and African-American riders were often treated unfairly and rudely. From the outset, Dr. King faced hostility from segregationists, and his life was threatened repeatedly. For example, during the bus boycott, his house was bombed, and he was arrested during a campaign to desegregate the city of Birmingham, Alabama (he was jailed several times during his lifetime).
Dr. King also faced life-long depression and the tension of uniting African-Americans and sympathetic whites into a movement that would achieve his goals. He advocated a policy of non-violence, inspired by ideas of Gandhi and others, and started the Southern Christian Leadership Conference (SCLC). In the 1960s, several civil rights groups developed, such as SNCC (Student Non-Violent Coordinating Committee). Leaders of SNCC thought that Dr. King was not connected with their concerns as younger members of the Civil Rights movement. Later leaders, such as Malcolm X, a Muslim, often believed in more direct and violent confrontations to achieve their aims than Dr. King did (though Malcolm X became more convinced of the power of non-violence before he died).
Another of Dr. King's challenges was to convince the federal government to become involved in helping the Civil Rights movement. At times, this pressure could take a long time to result in legal changes. For example, during the Montgomery Bus Boycott, the Supreme Court eventually passed a law (in December of 1956) that supported a lower court's ruling outlawing segregation in busing in Montgomery, Alabama. However, the boycott had already been going on for more than a year at this point, forcing African-Americans to walk or carpool to get to work or school. In addition, federal laws to protect the civil rights of African-Americans on a national scale took a long time to pass; finally, in 1964, the national Civil Rights Act was passed. The Voting Rights Act, passed in 1965, was passed to protect the rights of all citizens, including African-Americans to vote. This act was the result of a long period of pressure that the SCLC and SNCC and others had put on the federal government to protect voting rights. In addition, the movement had to endure a great deal of violence and hatred before this law was passed.
Dr. King also turned to issues that were difficult to solve. For example, in 1968, he went on the Poor People's Campaign to improve jobs and housing for African-Americans, particularly in urban areas. These issues were difficult to solve, and when Dr. King was assassinated in April of 1968, he was still trying to solve these types of difficult issues of economic inequality that are still present in the U.S. Therefore, Martin Luther King, Jr. faced enormous challenges, including violence, the problems of uniting his movement, the problem of pressuring the federal government for change, and the problem of inequality, among others.