Why did the u. s. senate ultimately fail to ratify the treaty of versailles
(specifically, the league of nations)? why were there dire consequences for
this decision?

The League of Nations was not ratified by the U.S. Senate because Republican members believed that the league was a supranational organization and would entangle the U.S. in alliances that it had sought to avoid since its founding. Also the Republican's believed the League of Nations bound the U.S. to certain principles that would not allow the U.S. to determine its actions for itself and therefore, it did not fully respect the sovereignty of the United States. Therefore, Republicans attached a number of amendments to the treaty and Wilson ultimately pushed Democrats to oppose the bill unless the amendments were removed, the treaty ultimately failed to be ratified. The lack of ratification can be seen as a potential cause of the instability and lack of a mechanism to deal with great power conflict that eventually led to WWII. 

Iwill support us side.