One would have to have actual borders in order to establish any control of immigration.
The United States effectively controlled immigration from 1921 when our "open borders" policies, at least with respect to Caucasians, were ended until 1964, when the national quota system was repealed. Of course, local authorities cooperated with the Feds in controlling immigration, which is not the case now, at least in California. Additionally, the courts of that era did not sense the existence of penumbras or emanations from the Constitution that granted extensive civil rights to those illegally in the United States.
It is obvious that neither major political party nor most political leaders have any intention of controlling immigration. Whether it is because of fear of antagonizing Hispanics and other minorities, the greed of businesses dependent on low wage immigrants and foreign trade, or a plan to permanently dislodge America's white majority, European-based culture, and Christian heritage is a matter of conjecture. The bottom line is that since 1964, the Federal government has not effectively enforced the immigration laws, nor is it likely to do so in the foreseeable future.