Final answer:
The primary objection to the Versailles Treaty by some U.S. Congress Members was the potential loss of U.S. sovereignty through mandatory participation in the League of Nations and threats to congressional war-declaring powers.
Step-by-step explanation:
The opposition of some Members of Congress to the Versailles Treaty was based largely on the idea that the Treaty would require the United States to join the League of Nations, which many feared might result in a loss of United States sovereignty. The concern was that Article X of the League's covenant could draw the U.S. into foreign disputes without the constitutional authority of Congress to declare war. Furthermore, the belief that British and French control over the League would supersede American interests added to the opposition.
The Senate, led by personalities such as Henry Cabot Lodge, was worried about the implications of Article X and the potential for overextension of American military obligations. This fear of entanglement in future European conflicts, along with concerns over sovereignty, led to the ultimate rejection of the treaty by the U.S. Congress. Without U.S. involvement, the League's potential for global influence and effectiveness in preventing future wars was substantially undermined.