"Of course, we could go down there and take half their country, just like we did in the 1840s."
From what I've learned from Mexicans, they're attempting to take back the land that they lost in the Mexican-American war. Just as the Israelites are being forced to give up Gaza and the West Bank, the Mexicans want us to give back those territories we gleaned from them in the war.
So we'll beat them in Mexican War II just as we did in Mexican War I.