In 1846 President Polk had a yearning for the U.S. to own territory from the Missouri River to the California coast.  The U.S. already laid (disputed) claim to Texas, but we wanted more.
Mexico at the time was a weak country, bankrupt and not able to control all its claimed territory, and a vast expanse it was, leading from the Missouri River to the east all the way to California in the west.  President Paredes of Mexico, recently a general and having wrested control of the Mexican government through other than democratic means, had nothing to negotiate with but was putting up a brave front.
Polk dispatched General Taylor with a small force to the Rio Grande near the Nueces River, the southern boundary of Texas at the time, to incite a response from Mexico for occupying disputed territory.  It didn't work... nobody came out to fight.  Commodore Sloat was dispatched to California to control the ports, and still no response.  What was Polk to do to pick a fight?
On 9 May 1846 a large Mexican force ambushed a small U.S. force, killing eleven, wounding five, and capturing the remainder, just in time to give the President his excuse.  President Polk dispatched forces, got money from Congress, and sent General Taylor to conquer.  Between General Taylor, General Scott, and Colonel Kearny, by October of 1847 the U.S. controlled territory as far south as Mexico City, and controlled that capital city by conquest.
President Polk had dispatched Nicolas Trist of the State Department with General Taylor early in the war with instructions to negotiate when the time came for Upper and Lower California (California and Baja), New Mexico, and Texas south to the Rio Grande.  And that is what Mr. Trist did.  But by this time it was obvious to President Polk he could ask for much more, and he sent word for Mr. Trist to be recalled in order to make new terms for Mexico down to the 26th parallel - a flat horizontal line on the globe ending at the tip of Texas.  Mr. Trist ignored the instructions, negotiated the Treaty of Guadelupe Hidalgo, and we ended up with the southwest U.S. as we know it now (short of the Gadsen Purchase).  A half million square miles bought for $15 million dollars (and $100 million spent on the war, along with 13,000 dead Americans).

But we could easily have had much more, perhaps all of Mexico and Cuba, too.  Certainly Mexico down to the tip of Texas.

Oh, well.  Who wants Guatemala as a neighbor, anyway.