At the heart of its dilemma is a man who was on that Memphis balcony with King when he died on 4 April 1968. He is Jesse Jackson, two-time presidential hopeful and now candidate to be leader of the most august US civil rights body, the National Association for the Advancement of Colored People (NAACP). Benjamin Hooks, its executive director of 15 years, was to have retired on 1 April, but has agreed to stay on temporarily: so contentious has been Mr Jackson's application that selection of a successor has still not been made.
Behind debate over 'Jetstream Jesse' - a label poking fun at Mr Jackson's often impetuous and mercurial style - is a wider uncertainty over the future of the NAACP and of the civil rights movement. Has the fire that was lit within it by King fizzled out?
Many argue that the NAACP particularly has lost its way, occupying itself so much with influencing government and currying favour with big business that it has lost touch with blacks in the streets. The impression was confirmed by a University of Michigan survey last year which found that, while most blacks wanted the NAACP to remain, they did not consider it relevant to their lives.
The feeling is shared by John Lewis, a Georgia Congressman, who was a close associate of King and a civil rights marcher. 'The NAACP is more at home signing agreements with banks and restaurant chains and utilities than it is looking out for the rights of individual black Americans,' he said.
Progress has undeniably been made since King's loss. The number of black elected officials in the country has risen from about 500 in 1965 to 8,000 today. Blacks have assumed the leadership of many cities. And roughly one third of black Americans now count themselves as middle-class.
Those achievements notwithstanding, the racial picture in the United States remains scarred. While some have found relative wealth, the situation for the poorest blacks, many dependent on welfare and marooned in decaying inner cities, is, according to some surveys, even worse than 25 years ago. Their problems are drugs, violent crime, illiteracy and single parenthood.
Nor can blacks claim any longer to be the only minority facing social hardship. By some reckonings Hispanics will overtake blacks in terms of population by the year 2000 and they share many of the same problems. 'Too often white people speak of civil rights in black and white terms but these days it is anything but that,' said Lisa Navarrete of the National Council of La Raza, the leading Hispanic rights advocacy group in Washington.
According to Ed Dorn, a scholar of racial politics at the Brookings Institution, the time has come for the civil rights movement to take greater account of these changing demographic factors. 'It no longer makes sense to talk about relations between blacks and whites in America; it's time we started talking in colour. Blacks don't have a monopoly on racial understanding,' he said.
And there has been a fracturing within the black community itself, with new tensions arising between those who have achieved prosperity and social status and those left behind. 'There is a now a vicious interaction between classes of blacks that is intractable for poor blacks,' says Mr Dorn.
Change also presents itself through the election of Bill Clinton and the passing of 12 years of Republican rule that was at least indifferent, if not openly hostile, to the civil rights agenda. Because of his Arkansas roots Mr Clinton can claim a greater sensitivity to minority concerns. His promise to reform welfare by forcing recipients to accept a job or training after two years may help to break the dependency cycle among poor blacks.
To some, selecting Jesse Jackson, with his charismatic appeal and high profile, to lead the NAACP would allow it to meet the new challenges. 'I think it would serve to send a very strong signal that the NAACP intends to become a more visible and more relevant organsation for black people. The organisation is at a crossroads and the choice of leadership will to a large extent determine its future course,' said Ronald Walters, a political scientist and former Jackson aide.
No one is prepared to predict what the 60- strong NAACP board will decide when it meets in Atlanta next week. Of the four finalists for the job of director, Mr Jackson, 51, is by far the best known. In the end, though, his energy and tendency towards controversy may be too much for an organisation that, to some, has become little more than a social club for ageing Selma marchers.