Depends when the PoD for this is.
1) If you have Eagleton get hit by a bus before he can slander McGovern anonymously to the newspapers, then there will be no "acid, amnesty and abortion" rumors, and it will be much easier for working-class Democratic voters to rally behind McGovern. (He favored amnesty, but the other two are twisting the truth - he was pro-life and believed in drug decriminalization, not legalization.) Then the party would be kept together and he'd actually have a very good chance of winning the Presidency with Ted Kennedy as his running mate.
2) If Kennedy agrees to serve as McGovern's running mate at the convention, he'd still have a shot: the polls for that hypothetical ticket against Nixon were relatively impressive, and an urban Catholic would help unite the party and dispel the image of McGovern as a candidate representing solely blacks and students. It would be an uphill battle, but it could result in victory - and even if it didn't, it wouldn't be a total landslide. If Kennedy accepts quickly, the convention could be wrapped up with little trouble, and then McGovern would be able to make a prime-time speech without being delayed until the middle of the night by pissed-off delegates nominating Chairman Mao and Abbie Hoffman.
3) If the PoD is that Kennedy agrees to replace Eagleton after he drops off the ticket, nothing will really be accomplished. The D's might win a few more percentage points and do better in the Northeast, but that's it.