Pursuing a new career as an attorney, she worked for a year at the NLRB as an enforcement attorney. Dodd was later
censured by the Senate and lost re-election, and the
Supreme Court of the United States refused to review a lower court's ruling that the suit was improper. Murphy was confirmed by the U.S. Senate as the first female Administrator for the U.S. Department of Labor in its Wage and Hour Division in June 1974. In February 1975, when Murphy was sworn in to serve as the first woman to chair the National Labor Relations Board, President
Gerald Ford said he chose her as "the most qualified and best respected person" for the job and not because of her sex. The
AFL-CIO declined to oppose her nomination, noting that she had represented both management and labor fairly during her legal career. While on the NLRB, the five-member board handed down rulings regarding rules for
collective bargaining and union organization in the healthcare field, allowing separate
bargaining units for clerks, maintenance workers, medical technicians and nurses, in which Murphy cast the deciding vote. Harking back to her journalism career, she cast the only vote against a 1976 decision regarding the rights of newspaper employees to form unions, noting her dissent that the skills required to be a reporter were "the essence of professionalism". She was succeeded as NLRB chairman by
John H. Fanning in 1977 and served on the board until 1979 when she turned down an interim appointment by President
Jimmy Carter. ==Later legal career==