Final answer:
The two disputes during FDR's presidency involved opposition to the New Deal from both conservative and liberal critics, and significant challenges from the Supreme Court, resulting in Roosevelt's court-packing proposal.
Step-by-step explanation:
During Franklin D. Roosevelt's (FDR) presidency, two prominent disputes stand out. Firstly, FDR's New Deal programs faced significant opposition, particularly from conservative critics who believed these initiatives resulted in excessive government spending and interfered too much with business. They argued that the deficit spending policy put the country into too much debt. Secondly, FDR's policies also faced opposition from the political left, including liberals who felt the New Deal did not do enough to aid poor Americans. Beyond these political disputes, a major controversy arose with the Supreme Court, which struck down key components of the First New Deal. This led to Roosevelt's contentious proposal to pack the court in his second term, which aimed to add more justices to the Supreme Court to gain favorable rulings for his policies.