Final answer:
President James K. Polk was the leader who sent American troops into disputed territory between the Nueces River and the Rio Grande, leading to the inevitable conflict with Mexico known as the Mexican-American War.
Step-by-step explanation:
The American leader whose actions made conflict with Mexico inevitable was President James K. Polk. He sent American soldiers into the disputed region between the Nueces River and the Rio Grande, which both the U.S. and Mexico claimed as their own, setting the stage for the Mexican-American War.
President Polk aimed to fulfill the expansionist desires of the United States. While the annexation of Texas in 1845 and its admission into the Union was recognized, disputes over its southern boundary led to tensions with Mexico. Mexico asserted the border was the Nueces River, a historically recognized margin, yet the U.S. claimed the Rio Grande, encompassing much additional territory. This pursuit for expansion was also evident in the covert mission of John Slidell, originally a diplomatic mission which included negotiations to purchase parts of the Mexican northwest. The resultant Mexican outrage and the subsequent ordering of General Zachary Taylor into the contested area by Polk, led to the outbreak of the Mexican-American War after a skirmish occurred.
In essence, Polk's orders for U.S. troop movement into the land between the Nueces and the Rio Grande, along with the failure in diplomatic resolutions, precipitated the war—a war that would eventually lead to significant territorial gains for the United States at the expense of Mexico.