Final answer:
The division within the Democratic Party and the response to violence and protests in 1968 most likely cost Humphrey the election. Many liberals and antiwar activists were disappointed by his selection over McCarthy, while George Wallace's third-party candidacy attracted voters disgusted with riots and antiwar protests.
Step-by-step explanation:
The factor that most likely cost Humphrey the election in 1968 was the division within the Democratic Party and the public's response to the violence and protests during that time period. Many liberals and young antiwar activists were disappointed by Humphrey's selection over Eugene McCarthy and his failure to chastise the Chicago police for their violence. Additionally, the entry of George Wallace as a third-party candidate attracted voters who were disgusted with the riots and antiwar protests. These factors allowed Richard Nixon to win the election, especially with his support among white Southerners in the previously Democratic South.