Depending on what period they arrived, most European Jews had to come through legal channels. Families were often separated for years until arrangements could be made for everyone to get to the U.S. And today, it’s no secret anymore what the State Dept. did and did not do before and during the Holocaust. But in general, the concept is and was that the U.S. was build by immigrants.
There are however, some mitigating circumstances nowadays. The border with Mexico is practically a fiction, a border only in name. As others have already remarked, there are many spots where people can and do just walk or swim over. The federal govt. has got to take control of the border. This also has national security ramifications as well, e.g., terrorism, chas ve’shalom. Exactly how to do this is not simple. A wall for instance can be easily circumvented by digging tunnels — something the smugglers are already doing. Seismic detection monitors could be deployed along the border, although this is probably horrendously expensive. Most likely a combination of air, land, and underground surveillance and detection systems will be needed, along with a seriously upgraded border patrol.
There is another angle concerning the illegals from Mexico. In certain locales, they are coming to the local and state governments demanding Spanish language services, road signs, and in some places parallel Spanish language classrooms in the public schools! True, lately some of these outrageous demands have abated, but it’s very often on people’s minds. Some Latino leaders in the U.S. (legal or otherwise) have even declared publicly that this is a way to “reconquer” land that used to be Mexican territory…. One Latino activist was asked why he insists so much on retaining Spanish, replied, “well, national pride, you know!” National pride??!! Spanish national pride is south of the border! In the U.S. of A, we are Americans who speak English! At home, church, the community center, at Cinco de Mayo celebrations, fine, speak Spanish. But at work, in the schools, on the highways — it’s America where English is spoken. BTW, with the Yidden who immigrated to the U.S. it was the same. They maintained Yiddish at home, in shul, sometimes in schools, etc. But everyone learned (or at least tried to learn) English. So the grandparents spoke with an accent, and the kids sounded American. I am not advocating being “a Jew in your home and a man in the street” kind of thing. Cultural identity is very important, particularly for Jews. But it’s important not to allow a gigantic sub-culture that excludes speaking English and much of the American way of life to develop. Maybe it’s already too late. But taking control of the borders would be a huge step in stemming the uncontrolled influx of many who resist becoming Americanized. Bottom line: yes to LEGAL immigration.