The death of Mary Jo Kopechne in the Chappaquiddick incident had greatly hindered Kennedy 's future presidential prospects , and shortly after the incident he declared that he would not be a candidate in the 1972 U.S. presidential election . Nevertheless , polls in 1971 suggested he could win the nomination if he tried , and Kennedy gave some thought to running . In May of that year he decided not to , saying he needed " breathing time " to gain more experience and to take care of the children of his brothers and that in sum , " It feels wrong in my gut . " Nevertheless , in November 1971 , a Gallup Poll still had him in first place in the Democratic nomination race with 28 percent . George McGovern was close to clinching the Democratic nomination in June 1972 , when various anti-McGovern forces tried to get Kennedy to enter the contest at the last minute , but he declined . At the 1972 Democratic National Convention , McGovern repeatedly tried to recruit Kennedy as his vice presidential running mate , but Kennedy turned him down . When McGovern 's choice of Thomas Eagleton stepped down soon after the convention , McGovern again tried to get Kennedy to take the nod , again without success . McGovern instead chose Kennedy 's brother-in-law Sargent Shriver
1972 Democratic National Convention
1972 Democratic National Convention
Ted Kennedy