Final answer:
Roosevelt's opponents characterized his concept of liberty as fascist and socialist, and they feared his New Deal policies threatened democracy, states' rights, and social order, especially with the federal government's increased intervention in the economy.
Step-by-step explanation:
Roosevelt's opponents criticized his notion of liberty by equating his policies with threats to democracy and American values. The American Liberty League and other conservative groups such as the National Association of Manufacturers aligned themselves against elements of Roosevelt's New Deal, which they labeled as fascist and socialist, contravening the core principles of freedom and democracy. These opponents were particularly disturbed by federal programs that seemed to impinge on states' rights and by the support for organized labor, such as collective bargaining, that could potentially undermine business interests.
Their criticism was also influenced by racial and class-based fears, especially in the South, where the expansion of federal power through the New Deal was seen as a threat to the existing social order. Aspects of Roosevelt's policies, such as his approach to the coal strike and the ideas behind the New Nationalism, suggested an unprecedented level of federal intervention in the economy and society, which was alarming to many conservatives at the time.