The U.S. withdraws from Vietnam, & all of Southeast Asia goes communist. Japan & NATO make side deals w/ the Soviet Union as the U.S. disarms in the name of peace. As the Soviets begin to take advantage of the power vacuum, the U.S. economy is hit w/ hyperinflation due to McGovern's socialist economic theories. McGovern is defeated in a landslide in 1976 by Ronald Reagan.
In actuality, yeah, though, it really is as unlikely as people think.
Nixon was a cynic & a criminal, but he had astutely pivoted on foreign policy: making token troop withdrawals from Vietnam, hinting at negotiations w/ Hanoi, launching the opening to what he used to call Red China, pursuing detente w/ the Soviets. The war raged on, but w/ fewer American, if not Vietnamese, casualties. Nixon's standing (not to mention the Eagleton fiasco) just showed too much of a good deal in the way of McGovern winning, plain & simple. Hence why he was duly crushed.
And just to be clear, Nixon wasn't invincible per se in 1972. It's just that no matter how you slice it, McGovern wouldn't have been the candidate to beat him. You'd need somebody competent, like Humphrey or Muskie, as the Democratic nominee to topple him.