Short Answer 
The New Deal, initiated by Franklin D. Roosevelt, aimed to revive the economy during the Great Depression with liberal policies that garnered support for the Democratic Party. Additionally, the Dust Bowl led to a migration of Midwestern farmers away from Republican loyalty, resulting in a significant shift in political support towards Democrats and reshaping the American political landscape.
Step 1: Understanding the New Deal
The New Deal, initiated by President Franklin D. Roosevelt, was a series of programs and reforms aimed at revitalizing the economy during the Great Depression. It introduced liberal policies that promoted social welfare and job creation, which resonated with many Americans struggling at the time. The impact of these reforms led to a surge in support for the Democratic Party, solidifying its power in both federal and state governments.
Step 2: Analyzing Demographic Shifts from the Midwest
During the Great Depression, the Dust Bowl severely impacted agriculture in the Midwest, forcing many farmers and their families to migrate. These individuals, facing economic hardship, began to turn away from traditional Republican loyalty and sought out a party that understood their struggles. As a result, a large number of Midwestern farmers shifted their allegiance to the Democratic Party, contributing to a significant realignment in political support.
Step 3: Recognizing the Impact of these Events
The combination of the New Deal and the demographic shifts created a major political realignment in America. This shift was characterized by a new base of support for the Democrats, primarily comprising urban workers and displaced farmers. Together, these elements redefined the political landscape, resulting in the Democratic Party maintaining substantial influence in American politics for years following the Depression.