The thing one has to remember is that
Basically as the title says. If Henry Clay instead of James K Polk is elected in 1844 or some other thing happens to halt American expansionism/Manifest Destiny for a time (you decide), what happens to the territories that would have become the American West in OTL? Specifically Texas (if it is kept from annexation), the Four Corner States (Arizona, Colorado, New Mexico and Utah), Oregon, and California?
EDIT: Oops wrong forum.
The thing one has to remember that is the U.S. gained its independence in 1783 and had been building itself up, as a centralized nation state, since then; Mexico only gained its independence from Spain as such in 1821, and even, the Spanish actively attacked Mexico as late as 1829; the true national consolidation phase, in terms of government, a national economy, construction of national institutions, stability, etc began at least four decades earlier in the U.S. than in Mexico, arguably five decades.
So, when it comes to competition between the U.S. and Mexico over what was (at the time) the Mexican Northwest, which became the American Southwest, the U.S. has a lead in terms of organization and all that means in terms of political, military, and economic strength of upwards of 40 to 50 years over Mexico.
That is not a differential that is going to be negated by policy makers, per se, on either "side."
And given that the founders of the U.S. had been on the front line, so to speak, of the great conflict between Britain and France over control of North America, they knew full well what a continent without a dominant power would look like, and conducted themselves accordingly; their equivalents in Mexico, since Spain did not have a great power rival in the Western Hemisphere in the same way, did not have that sort of foundational lesson.
Best,