Final answer:
Roosevelt faced strong criticism from both conservative and progressive critics over his New Deal policies, but he maintained popularity and adapted to challenges, including Supreme Court opposition.
Step-by-step explanation:
Strong political challenges to Roosevelt came from an array of extremist critics who were unsatisfied with his New Deal policies.
On one hand, conservative critics, including industrialists and the American Liberty League, accused Roosevelt of moving the country towards socialism and fascism, and undermined his policies like the Agricultural Adjustment Act (AAA) and the National Industrial Recovery Act (NIRA) which they considered overreaching federal authority. On the other hand, progressive critics like Upton Sinclair, with his "End Poverty in California" program, argued that the New Deal did not go far enough in addressing poverty and economic inequality, advocating for more radical reforms such as a progressive income tax and a pension program for the elderly.
Despite the criticisms, Roosevelt managed to maintain his popularity among the American public and win reelection in 1936. Even after the U.S. Supreme Court struck down key pieces of the New Deal as unconstitutional, Roosevelt was able to subsequently appoint more sympathetic justices to the court, reaffirming his strategic adaptability in the face of opposition.