Complex sentence: John F. Kennedy's administration proposed the President's Commission on the Status of Women to address people who were concerned about women's status while avoiding alienating the Kennedy administration's labor base through support of the Equal Rights Amendment.
Split into simpler sentences: John F. Kennedy's administration proposed the Presidential Commission on the Status of Women as a "compromise" measure. It would address people who were concerned about women's status while avoiding alienating the Kennedy administration's labor base through a potential mention of the Equal Rights Amendment.