Of course the beauty of the system is that the number of representatives in the House would not change (as is mandated by law). Only the size of the Districts. I understand your point about the perception that the Mexican citizens would be prone to vote Democrat, but they are by-and-large much more conservative socially than most people allow. At many levels it's a simple trade - your resources (natural and human) for our structure and organization.
There are lots of Mexicans (legal and illegal) voting in California. If these people were an asset to the state, I wouldn't expect California to be near bankruptcy.
Many are very Catholic and to some extent this makes them social conservatives. They generally are family oriented and oppose abortion. But their social conservatism is somewhat overrated. Take a look at the statistics for single, unmarried mothers and you will find Hispanics among those with the highest growth rates. They also are more likely to be opposed to military spending and anything to do with law enforcement. Their overlap with our traditional conservative values including things like personal responsibility is rather narrow.
And people tend to vote for social issues as a luxury only after they feel comfortable economically. A good measure of how Mexicans in Mexico might vote is how Mexicans in America vote. They have for years given the vast majority of their votes to Democrats and about the best we have ever done with them is the 38% to 40% of the vote which Bush got in the most recent election. Keep in mind that the National Hispanic vote is considerably influenced by the Cuban vote which goes heavily Republican. Without the Cuban vote, Mexican-American Hispanics would have been a much larger factor and the results for Bush would have looked much worse. The propensity for Mexicans to vote socialist are confirmed by the current political situation in Mexico. By far the most popular national politician is the flaming leftist Mayor of Mexico City. Without a major sacrifice of our principles and values, Republicans would do poorly in Mexico.
Of course the beauty of the system is that the number of representatives in the House would not change (as is mandated by law). Only the size of the Districts.
Which means that about 25% of the power would shift away from the current 50 states to Mexico in proportion to their population. Even worse, they would have almost a 25% share of the electoral vote. It would be almost impossible for a President to win without carrying a good portion of Mexico and that would mean that Democrats would control the Presidency for the foreseeable future.
I repeat, annexing Mexico would be national suicide. They have some nice real estate but unfortunately it is full of poor people who would vote for Democrats.