Constance was born in Howland, Maine, a paper mill town, as one of two children to Clifford and Edith Burglyne Nash. Her girlhood home stood on the banks of the Penobscot River, where the family kept a vegetable garden, which Constance helped to maintain. Her father worked at the paper mill, but it closed during the Depression. He turned to timbering, staying "a week up in the woods earning a dollar a day," Constance recalls. As a teenager she worked after school for her Sunday School teacher and her husband, cleaning house and getting dinner started. She received three dollars a week. Constance graduated from high school in 1942. Hoping to enter nursing school, she went to work at New England Baptist Hospital in Boston, first as a nurse's aide. She lived in a nurse's home, worked 12 hours a day at the hospital and attended classes for nurses training. She had won a scholarship that paid her tuition. While working at the hospital she met John F. Kennedy, recuperating after injuries in the Pacific, while he was walking in a corridor wearing only a bath towel. She recalls telling him, "Jack if you come out in the corridor you got to put a bathrobe on." She got along well with the future U.S. senator and President of the United States, she recalls. "I thought he was nice. We didn't have to do much for him because he really wasn't that ill." She also met his mother and brothers Teddy and Bobby. In August of 1945 Constance joined the U.S. Cadet Nurse Corps. "They wanted to make sure they had enough nurses to man the facilities as long as the war lasted," she says. Her basic training at Camp Devens in Ayer, Massachusetts, lasted only two weeks. "It was a laugh," she recalls. She was then sent to a hospital at Camp Edwards where she worked in the hospital for six months, where many of the patients were casualties from the China-Burma-India Theater, "because that was the last fighting place we had," she says. She enjoyed working in the operating room, and wanted to be a scrub nurse. Assigned to an orthopedic ward, she met her future husband, William Edward Parker, who had been wounded in a heel soon after the Battle of the Bulge. While Constance returned to New England Baptist in February of 1946, William soon entered Brown University in June of 1946 studying to be a chemical engineer. The couple married on September 6, 1947. (They would have three children, four grandchildren, and four great-grandchildren.) William graduated in January of 1950. Constance worked as an RN at hospitals while William advanced in his career and his education earning a Ph.D. in 1956. The couple would eventually live in California, Delaware, and New York. In 1996 they moved to Blanchard, Louisiana to be near a daughter and granddaughter. William passed away in 2001.