The government would remain a USA constitutional government. Maybe we can repeal the 17th amendment while we're at it to give the states back some of their local power. This might entice some of the Mexican states that might otherwise think that they will be lost in the "inside the Beltway" silo of Washington DC. We would also need to make a one-time exemption to allow all foreign-born citizens at the time of ratification to be eligible to become President.
On the plus side, all illegal Mexicans in the USA would automatically become citizens by virtue of Mexico joining the Union. If we want to build a wall, we can do it at the new USA/Guatamalan border.
-PJ