This idea is not a "new idea" in the 21st century. This idea against immigration has been with us since the dawn of this country. For example, Benjamin Franklin disliked immigration as he wrote about it. Moving forward in the 19th century, it got worse. Irish immigrants were discriminated against because they were Catholics, and the Irish themselves were not treated well in the United Kingdom as well(there was not any "Northern Ireland" and "Republic of Ireland" in the 19th century yet). So when the Irish came to the United States, the Irish were still exposed to the Anglo-Saxon values from the Old World. The United States has Anglo-Saxon values which were not forgotten or lost because it was founded on such values, and it showed when it came to the New York Times. In the 1850s, the Irish could not apply for many jobs because the advertisement wrote "No Irish need apply". They were not even allowed in parks in Boston.
Immigration causes panic in our American history because people fear about "changing the country" so to speak, and the "Know Nothing" Party of the 19th century was one political party in the United States which was anti-immigration. Not only that, but the eugenics movement was a big influence in the 19th century because many people thought that Anglo-Saxon individuals were more advanced than "other races". People who were into eugenics thought "other races" would "pollute" the population, and this was one reason why immigration had to be limited. Therefore, in the early 20th century, there were quota systems put into law so they would limit immigration into the United States.
Even though we are more "pluralistic" now, there are still "these fears". We came more "pluralistic" from the Cold War because we had to control the spread of communism more, and this helped in bringing in Asian immigration into the country, hence forming the "model minority" stereotype. The Civil Rights movement also helped as well as getting rid of the quota system during Lyndon B. Johnson's presidency. Nevertheless, these fears of immigration in the 21st century still linger from our American past.