Conservatives challenged Roosevelt's leadership and New Deal programs because they thought that Roosevelt's new economic policy was based on socialism.
Explanation:
Roosevelt's 'New Deal Programs' included a series a of programs which embraced the idea of government intervention and control of the economy. It also raised taxes. and formulated new commerce laws.
These activities made the conservatives to question and challenge Roosevelt's leadership and his 'New Deal Programs".
The conservatives felt that the country was driving towards a socialist economy where the government controls the whole economy. They feared that capitalism was at risk.