Irredentism can be a powerful force in politics. Hitler used it as an excuse to annex Austria, the Sudetenland, Alsace-Lorraine, and parts of Poland. Stalin, though theoretically an internationalist, strove to restore the boundaries of the Tsarist Empire in Eastern Europe. While there is a lot of anti-Americanism in Canada, the Canadians and British successfully repulsed American invasion attempts during the Revolutionary War and the War of 1812. OTOH, Mexico was humiliated by the loss of Texas, and later of the rest of the Southwest, in the 1830s and 1840s. American response to Mexican incursions was swift and forceful in the 1910s, when the U.S. Navy captured Vera Cruz and the U.S. Army invaded northern Mexico to stop Pancho Villa's cross-border raids.
It is self-evident that the American government and people do not have the will to resist that their predecessors did. Starting in 1965, immigration laws were liberalized, and the 1986 amnesty program essentially forgave a past generation of illegal immigrants. Mexicans and others have recognized the softness on the part of the United States. Cities like Los Angeles and areas like the Rio Grande Valley that were once more mixed ethnically have become more and more Hispanic. When a population becomes sufficiently large that they have their own cultural and media infrastructure and little contact with outsiders, there develops little desire for assimilation. There is precedent for long standing non-English speaking communities in America. Some farming communities in Pennsylvania and the Midwest settled by Germans remained German speaking until well into the last century. Additionally, Cajun communities remained French speaking until after World War II.
Much has been made about how Italians, Poles, Jews, Greeks, etc., who arrived in the 1880-1920 immigration wave became Americanized, as of course they did. However, an important reason for their assimilation was the restrictions placed on immigration following World War I. With the flow of immigration ended, there were no new immigrants who would keep their predecessors current on the culture and politics of the old country. Additionally, the immigrants in question had arrived legally and by having this status, they did not enter the country already at odds with the authorities.
The immigration from Latin America, especially Mexico, is more like what happened in Kosovo where Albanian immigrants became a majority in the last century. By the 1990s, rather than submit to the Serbian authorities, they rebelled and established their own government, expelling the remaining Serbs. Continued unchecked immigration will cause a similar situation to develop in the Southwest.
Instead of engaging in a multitude of activities, the vast majority of which were never intended by the Founding Fathers, the Federal government must engage in its Constitutional duty in protecting our borders by whatever means necessary.
Perhaps I put too much faith in the power and appeal of American Materialism, but it has worked to assimilate other generations of immigrants; I see no particular reason for it not to work again.