Mexico was politically unified under its president, had a larger army, was on the defensive terrain very far away from American logistics and had European support (who would be interested in keeping the Balance of power). Not sure how the Americans could win decisively here.
Plus James Polk's Pacific ambition was mainly focused on the Oregon Territory and Columbia, which he got... not to mention the thin border strip, the Jefferson purchase, to allow a railroad to Oregon. So why would he even want to attack Mexico?
Why would he even want the Gran Lago Salado territory or the southern two thirds of Alta California, or any piece of Nuevo Mexico? Why jeopardize the relationship between the Mexican Presidency and the United States of North America, just for a strip of desert, which was not yet known to be mineral-rich?
Now if a small scale war broke out in the Jefferson Territory due to the Gold Rush on the US Mexico border, that I could understand. But that's 10-15 years after Polk. And that was skillfully defused by Archbishop Santa Anna and Ambassador Abraham Lincoln, so you have to get rid of those two figures for war to break out.
Truly it would require something ridiculous like Mexico allowing Americans to settle Tejas or something.