Nothing is "automatic" just because you marry a Mexican. You must still meet the immigration requirements for some specific status. A tourist permit has no income requirements but is only good for a maximum of 180 days; and they don't have to give you that if they don't feel like it. It is not renewable in Mexico and requires that you leave the country.
Mexico is a wonderful place to live if you have financial resources from outside the country. Mexican wages, if you could manage to get permission to work, are a tiny fraction of US wages and, unless you could 'pass for Mexican', you might find life quite difficult in the workplace. There is also a nickname for 'gringo' husbands; "The Wallet". You really need to visit, meet the girl's family, study the situation in detail, and evaluate the options very carefully. I have strong feelings about this because of a similar situation in my wife's family which turned out badly. There are now children who can never cross an international border until they are 21, as a result. Please be aware of all of the implications.

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Read "Streets of Glass" to discover the experience of a retired couple's permanent move to Lake Chapala, Jalisco, Mexico.
PM for details.