Had the US held a referendum in the Mexican Cession in 1848, who would have won this referendum?

Futurist

Ad Honoris
May 2014
18,701
SoCal
#1
This would have been really out of character for the US, but let's say that Mexico would have experienced more successes on the battlefield in the Mexican-American War and thus Mexico and the US would have eventually agreed on the idea of holding a referendum in the Mexican Cession in 1848 in order to determine its fate. If such a referendum (completely free and fair, and with all free adult males other than perhaps Native Americans being eligible to vote in this referendum) would have been held, who would have won this referendum? The US or Mexico?