“Reconquista” is a term used for the belief, held by some Mexicans or people of Mexican origin (and/or attributed to them), that the southwestern United States should legitimately belong to Mexico, and the movement of Mexicans across the southern U.S. border is a step toward the reconquest of this area. Here is the Wikipedia entry on the subject.

Restrictionists have used claims of the prevalence or incidence of Reconquista to argue that the continued arrival of Mexicans in the United States will lead to foreign control and loss of sovereignty. Restrictionists also point to what they perceive as high and growing interference by the Mexican government and embassy in U.S. laws on the grounds that these laws affect Mexicans or people of Mexican origin.

Restrictionist writings on Reconquista

• Memo From Mexico | You Say You Want A Reconquista? by Allan Wall, July 5, 2007, for VDARE.
• Welcome to Reconquista by Michelle Malkin, March 27, 2006, on her blog.
• The Reconquista Movement: Mexico’ Plan For The American Southwest in Human Events.