Final answer:
The significant realigning event between 1860 and 1932 was the 1932 presidential election, where Franklin Delano Roosevelt's victory led to a long-lasting political realignment in the United States.
Step-by-step explanation:
The realigning event referred to between the years 1860 and 1932 is most likely the 1932 presidential election and the subsequent formation of a new political alignment under Franklin Delano Roosevelt. This election saw the Democratic Party's transition towards being a political force that sought to include those hurt by the Great Depression, including African Americans, as part of its new coalition. This realignment resulted in a long-term shift in voter allegiances that shaped American politics for decades.
Roosevelt won the election with a sweeping majority, marking the event as a critical election – a definitive shift in political alliances based on socio-economic preferences. This shift solidified the Democratic Party's influence in American politics, with the party winning several consecutive presidential elections and dominating Congress for many years. The strategy of including various socio-economic groups changed the landscape of American political alignments, with far-reaching effects on the Democratic Party.