Final answer:
The conflict between the United States and Mexico intensified tensions over territorial issues, fueling sectional debates about slavery in the acquired territories, and necessitating the Compromise of 1850 to address the balance between slave and free states.
Step-by-step explanation:
The conflict between the United States and Mexico increased the need for compromise because it intensified tensions over territorial issues. The culmination of the Mexican-American War and the ensuing Treaty of Guadalupe Hidalgo in 1848 brought a significant amount of territory into the United States. This acquisition raised questions about the expansion of slavery into these new territories such as California and New Mexico, intensifying the national debate. Southerners wanted the newly acquired lands to allow slavery, while Northerners opposed this expansion.
The conflict and resulting territorial gains upset the balance of free and slave states as established by the Missouri Compromise, leading to sectional tensions and a series of events that sought to address or exacerbate these issues, like the Compromise of 1850 which attempted to ease the tensions by dealing with the status of the new territories. The Compromise included measures such as strengthening the Fugitive Slave Act and deciding the status of slavery in the District of Columbia amongst others. However, events such as the Kansas-Nebraska Act and the Dred Scott decision only increased hostilities further, leading the country closer to civil war.
In addition to slavery issues, the war and resulting land cessions also led to racial antagonisms and violence, as Mexicans and Mexican-Americans were dispossessed of their lands, with their land deeds declared “imperfect” by the U.S government. This pattern of violence and racial antagonism has had long-lasting effects. Therefore, the correct answer to the conflict's impact that increased the need for compromise is 'It intensified tensions over territorial issues'.