What if Mexico accepted James Polk's Request to purchase the disputed Texas border?

In 1845, newly-elected 11th U.S. President James Polk made an offer to the Mexican Government to purchase the disputed lands between the Nueces and Rio Grande Rivers. When this was rejected, it set off a series of events that lead to the Mexican American War.

What if Mexico had accepted Polk's proposal? What would America pay for the land between the rivers? How would this affect America and Mexico? Additionally, how would it affect other organized rebellions in Mexico such as the Republic of Rio Grande and the Californian Republic?
 
It's gonna be hard to convince Mexico to do that. Mexico never stopped claiming Texas before the M-A War, and refused to aknowledge their claims (basically refuting the Treaty of Velasco, considering the circumstances of its signing). It's theoretically possible for a president to agree to sell the disputed area, but only if he's content of painting himself a target for pretty much every political and military enemy, and perhaps that of his own friends as well. Mexico has been refusing sale proposals since the 1820's. If that was when things were less tense on the matter, then during the 1840's after Texas breaking off and joining the USA and claiming land beyond their borders... it's borderline ASB.

But assuming that against all odds it does happen... well, actually, I'm not really sure what could happen. No M-A War, that's for sure. Or at least, no war because of Texas's border claims. The US will still have their eyes on the Alta California, and that can still result in war.

By the way, the Republic of Rio Grande thing started and died in 1840, so this is way after that. Bear Flag Republic might still happen, but without the M-A War as a distraction, it might fail. Or who knows, things in the south could still be busy with the coup and in-fighting that resulted due to selling the disputed area. But they'd be aware the Americans are trying to pull a Texas again, so who knows.
 
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