IOTL, McGovern offered Ted Kennedy the Vice-Presidential spot (Gallup Polls at the time showed McGovern losing to Nixon by only a 49-44 margin with Kennedy as his running-mate). By getting the popular Kennedy as his runningmate, McGovern also managed to avoid the Eagleton debacle (without the Eagleton debacle, he probably would have carried more than one state, even without Kennedy as his running-mate).
Suppose Wallace doesn't get shot in Maryland, and runs as a Third Party candidate again in 1972, as many people believe he would have done?
McGovern: 42%
Nixon: 40%
Wallace: 18%
I don't want to do the research on Electoral votes distributions in 1972, but let's say McGovern carries Massachusetts (a safe bet), Rhode Island, New York, Pennsylvania, Maryland, West Virginia, DC, Ohio, Michigan, Wisconsin, Illinois, Minnesota, Iowa, South Dakota, California, Washington state, and Hawaii. I'm pretty sure that would have put him over the 270 mark (using 2004/2008 EV distribution numbers, that would only give McGovern 249 Electoral Votes, but the Northeastern and Midwestern states had a significantly larger share of the EVs, so I'm almost certain that would give McGovern a victory based on 1972 EV distribution patterns, although I could always throw in New Jersey, Connecticut, Delaware, and maybe Oregon,* if necessary).
Additionally, I'm assuming that not only did Wallace carry the five states he got in '68 (Alabama, Mississippi, Louisiana, Georgia, and Arkansas), but also Florida and South Carolina (Goldwater and Thurmond both carried South Carolina, in '64 and '48 respectively, and I know Wallace came in second place in Florida; my aunt Peggy in Tampa even voted for Wallace in '68, and she was a transplant from Massachusetts, of course, my aunt Peggy always voted for 3rd party candidates, from both the left and right, bless her soul). So even in the unlikely event that the states I assigned McGovern do not give him a 270 EV majority, the election would then be thrown into the House of Representatives, where I tend to suspect the overwhelmingly Democratic body would select its own nominee to be President).
*Today we think of Oregon as a pretty "blue" state, but until Dukakis (of all people) carried in it 1988, it hadn't gone Democrat since the 1964, 44-state sweep for Lyndon Johnson, while Washington state had voted for Humphrey in 1968.