Interestingly... Kennedy's death in 1963 probably triggered the sudden halt in the baby boom. Births in late 1964 and into 1965 fell substantially. People were just not making babies in the brave new world that followed JFK's assassination. The era of optimism was over.
While that does make some sense, the birth rate peaked in 1947 and the total number of births peaked in 1957. It declined almost every year after that, the introduction of the pill in 1960 greatly accelerating the trend. I prefer to look at the rate per 1,000 population, instead of per 1,000 women. It seems news articles don't use this number anymore, which is annoying.
United States Birth Rate
1957 25.0
1960 23.7
1970 18.4
1980 15.9
1990 16.7 (Baby Boom echo)
2000 14.4 (Gen X being smaller than Baby Boomers, total rate declines.
2007 14.0 (Economy was pretty good from mid 2003 until this year, after birth rate had plunged during 01-03 recession
2013 12.5 (Great Recession: Millenials and Older Gen X'ers delay having children)