Don't forget that with Texas occupied fighting other states, their resources to guard the border with Mexico would be stretched pretty thin. I'm sure the cartels would seize the opportunity to move north. You'd want to protect the border at the same time you're fighting a war, and that would be tough. The same would apply to California to a lesser extent because of a smaller border.
That lack of a real justification for the war in the first place is what makes it hard to have any meaningful response to the topic.