MEDFORD, Mass. — JUNE 11, 1963, may not be a widely recognized date these days, but it might have been the single most important day in civil rights history.

That morning, Gov. George Wallace, in an effort to block the integration of the University of Alabama, made his futile “stand at the schoolhouse door.” That evening, Boston N.A.A.C.P. leaders engaged in their first public confrontation with Louise Day Hicks, the chairwoman of the Boston School Committee, over de facto public school segregation, beginning a decade-long struggle that would boil over into spectacular violence during the early 1970s. And just after midnight in Jackson, Miss., a white segregationist murdered the civil rights leader Medgar Evers.

But the most important event was one that almost didn’t happen: a hastily arranged speech that evening by President John F. Kennedy....