The average Mexican, I'm not sure. Why don't you mount a survey to find out? Any results would be somewhat interesting. Either way, the historical facts run counter to some groups alleged collective belief.
The Reconquista will likely be ignored unless or untill they try to seize something located in the Southwest that the Government deems of value, be it monetary or strategic. When they're having to face down a detachment of soldiers or marines, what they believe will truly come to the fore.