The official statistics on the number of federal employees (excluding army and postal service) between 1960 and 2005 are available at http://www.opm.gov/feddata/html/ExecBranch.asp.
The data only shows the numbers at the end of each fiscal year (which at the time ended in June), so if we take Kennedy's presidency as lasting roughly from the start of 1961 (although his inauguration was on January 20, a few months before the start of the fiscal year) to the end of 1963 (although he was assassinated a few months after the end of the fiscal year, in November), the data shows that the number of federal workers went from 1,807,958 to 1,910,538 (which is an increase of roughly 100,000).