However, voluntary repatriation was far more common than formal deportation and federal officials were minimally involved.[5] Some of the repatriates hoped that they could escape the economic crisis of the Great Depression.[9] The government formally deported at least 82,000 people,[10] with the vast majority occurring between 1930 and 1933.[5][11] The Mexican government also encouraged repatriation with the promise of free land.[8][12]: 185–186
This makes it seem like many of them wanted out of the US already, and Mexico was more than willing to receive them.
Edit: The page also says that people were blaming Mexicans and making them the scapegoat for the reason why they were dealing with the great recession. It seems that many were already wanting to move to Mexico due to the recession coupled with the promise of free land. There were still a lot who were deported forcefully against their will.
Reading the source article for that one is wild. Yes, many more were not "deported" but were instead "repatriated" but it is well documented that they were coerced and threatened into leaving.
If you are not obviously white (a la the aforementioned Family Guy color chart), and even if you are but live in a multiethnic area, do yourself a favor and get a passport. Carry it with you whenever you leave your residence.
I'm Asian American (born here) but have always been mistaken as Hispanic (ever since my early teenage years) and I'm already thinking of carrying my passport with me starting on Trump's first day.