The US had gotten what it wanted from Mexico in 1845. It wasn't interested in absorbing the more heavily populated areas of the Spanish speaking nation. The US was not naturally a colonial power. At the time it wanted the boundaries it eventually achieved during the administration of James Polk. It later bought the Gadsen Purchase for a railroad at about the same price as it paid for the Mexican Cession.
"The US was not naturally a colonial power"? So how on earth did a strand of agrarian colonies cross the Alleghenies to conquer everything between them and the Pacific? The colonies were slavering over the Ohio Country before the Revolution, and that slavering persisted after independence as the U.S. turned hungry eyes on the Louisiana Country, the Canadas, Cuba, the Floridas, Texas, California, various Pacific archipelagos, Cuba (again)...
True, the United States did not join the league of maritime imperial powers until the 1890s-1900s, but that was because it had spent every minute of its previous existence being a land empire that was largely concerned with the process of internal colonization, which usually entailed taking land from indigenous peoples who were then displaced or outright butchered by settlers, state militias, and/or the U.S. Army. Lest it be forgot, the "Frontier" was only declared closed by the U.S. Census Bureau in 1890. Unsurprisingly, U.S. imperialism would then turn outwards before decade's (and century's) end.
A word on the borders established following the Mexican-American War: They were
not what the United States wanted in 1848. After the lightning victory of U.S. arms over Mexico in 1847, a large faction of the ruling Democratic Party wanted the United States to annex the whole of Mexico, not just those of its northern territories which would connect the United States with California.
President Polk himself had pronounced sympathies for the "All Mexico" movement, and the borders he himself laid out (image below) were somewhere between "All Mexico" and the final settlement of Guadalupe-Hidalgo.
It should be noted that the terms laid out in the treaty of Guadalupe-Hidalgo were something of a
fait accompli. There was enormous pressure within both the Congress and the American electorate to end the war, whatever the terms, and quite a lot of that faction preferred no territorial gains from the war whatever. More than that, the treaty had been negotiated by a diplomat whom Polk had recalled, only to receive a 65-page letter from the envoy (one Nicholas Trist) informing Polk why he was ignoring the president's orders and continuing with the negotiations, official sanction or no. By the time a furious Polk received the treaty of Guadalupe-Hidalgo in February of 1848, the anti-war fervor had only grown (as had the cries to annex all Mexico), and there were serious concerns over whether there would be any Mexican government to negotiate with if the treaty were rejected, as the Mexican Congress's legitimacy was on shaky ground within Mexico itself, as a quorum was difficult to achieve in the temporary capital of Queretaro, and a defiant Santa Anna was still loose the country at the head of an army. Given the many signs that this may be the
only chance for a U.S.-Mexican peace, Polk reluctantly agreed and sent the treaty to the Congress. (Which body would have been outraged had the president sought to keep the treaty from it.)
After sending the treaty to Congress, Polk nevertheless attempted to get Congress to approve a humanitarian intervention in Yucatan and establish a U.S. protectorate there (John Calhoun was the foremost Congressional opponent of this scheme), and further attempted to purchase Cuba from Spain for the sum of $100 million. Franklin Pierce Southern sympathies would also seem him adjust the U.S. borders in Latin America, whether it be another attempt to buy Cuba, or the successful Gadsden Purchase, which had been secured to ease the forging of a transcontinental railroad on a Southern route.
