When you are a president it is always good to appear fair and diplomatic. This is why the presidents wanted to buy the land. Thomas Jefferson bought his land from France in the famous Louisiana purchase. It was a bargain brought on the table by France for many differing reasons. Polk on the other hand fought Mexico in a war. Then once he owned the land gave them only a portion of what it was worth. He had leverage over the Mexicans because he had crushed their armies in the Mexican war.
Its hard to escape the presidency without some scandal. Polk and Jefferson both could not accomplish this. Jefferson bought the Louisiana purchase from France. Even though he believes and, at the time it was widely believe he shouldn’t have that power. Polk’s on the other hand was more substantial. He sent troops into either America, Mexico or, the disputed territory and they were ambushed prompting the war. If the troops were in the disputed territory then they might declare war. If they were in Mexico what Polk did was illegal. IF the troops were in Texas then it is all out war. Polk never clarified where the troop were to we may never know.
During Jefferson’s and Polk’s presidencies America wasn’t really a world power. So when America got the chance to take land they took it quickly. Jefferson when offered the Louisiana purchase acted quickly so the French might not change their minds or some other country would take the weakly guarded land. Polk also was afraid that the Russians or the British might swoop down and take California. Something Polk couldn’t afford.