Final answer:
The strongest argument in the Congressional debates over slavery depends on perspective, with the Republican Party making ultimately impactful arguments that aligned with the historic trend away from slavery.
Step-by-step explanation:
Who made the strongest argument during the Congressional debates over slavery is a subjective determination, often influenced by individual beliefs and values. During the expansion of slavery post-U.S. victory over Mexico, arguments varied greatly, and significant moments such as the altercation between senators Benton and Foote catalyzed public interest. The debates leading up to the critical presidential election of 1860 saw the Democratic Party fragmented by internal divisions on slavery, while the Republicans capitalized on a unified stance against it.
Congressional polarization increased over time, with the middle ground of compromise diminishing as the parties grew more ideologically extreme. Throughout these debates, the most compelling arguments depended on the perspectives of their audiences, making it difficult to declare an objective winner. However, in the context of historical impact, the Republican Party's stance which contributed to their eventual victory in 1860 provided an enduring legacy, as it aligned with the national shift away from slavery.