This may require 20/20 hindsight on King's part, but I don't think it's possible to support a government program as a temporary measure. Once instituted, it is so difficult to end a program, that we have to look at every one we support as permanent.
Note too that virtually all civil rights leaders supported quotas, without any notion of them being temporary, and Justice Thurgood Marshall privately told people 30 years ago, that AA would be necessary "for 100 years," which is just another way of saying, "forever."
Hindsight? King lived in a time (as did my parents who grew up in Miss.) when there was NO justice for a black person. To them, injustice was just too real. King's generation took the best chances they could get to seek any sort of balance.
Marshall was radical. But remember, that generation SAW things that would absolutely unacceptable today (ie. James Byrd's murder) and often nothing was done at the time.