Maybe this is ASB, but one idea I had would be is if the Civil Rights Act fails to pass. This leads to massive levels of unrest in Black-majority cities in both the north and the south led by black radical groups during the mid-1960s. This creates an equally massive white backlash, which turns America into a bloodbath resembling Northern Ireland in the 70s or Bosnia in the 90s. As a result, Wallace gains much more support than OTL among white voters in the northern states that have substantial black minorities. Wallace runs on an openly pro-segregationist platform, advocating segregation in the north as well as the south, to play on racist sentiments of Northern whites (if you think this is farfetched, consider how much geographic segregation exists in Chicago, Milwaukee and Detroit even to the present day).
If Wallace won a plurality, the election would go to the House, which has a majority of state delegations that would favor the Democratic candidate (if my understanding of the 12th Amendment is correct). Thus, I think Wallace would have to receieve more than 270 electoral votes. In order for Wallace to win the electoral vote outright, he'd not only have to win the entire South (155 electoral votes), he'd need to win every state where he received more than 9% of the vote in OTL (most of the Midwest and West). For that to happen, both the Democrats and Republicans would have to nominate candidates that would be unappealing to white working and middle class voters in both parties (say Eugene McCarthy for the Democrats and maybe Nelson Rockefeller for the Republicans). By my rough calculations, Wallace could win with roughly double the number of votes he received in OTL, concentrated mostly in the Midwest and the Southern states he didn't win in OTL.