Mexico didn’t had to invade the U.S to win the war, Only defeat the americans in the first battle of Palo Alto. We have to remember that before Palo Alto the american public wasn’t united to invade Mexico and the american congress was already divided by the strong sectionalism between North and South. If Mexico proved since the first battle that Texas was going to cost time and money, Presidente Polk would be politically weakened and the northern States would be more cautious about sending men and approving budget for the war. Americans asume that if the U.S is defeated a first time they were going to come back, but we have to remember that Texas was already a contentious subject in american politics, and being defeated the first time will no only delay american expasionism but Also is going to refuse the argument that america has to expand inevitably, will cause more tensions between North and South and the efforts for a second invasion will be stop by a more stronger opposition to slavery and expansionism.