I will point out that the book by Peter Brimelow, called "Alien Nation" came out in 1995 and was in paperback in 1996. If you have read this book, as I have, you will thus be aware that the problem of illegal immigration was something that people were well aware of in 1996.
It depends which people. I read Jean Raspail's "The Camp of the Saints" in 1973, when it came out. I was also concerned way back when they changed the immigration laws. And I didn't like Reagan's amnesty.
But if you are talking about ordinary people, and the great majority of voters, then I think they have only recently started to become aware of the problem.
Obviously it also depends where you live. Immigration used to be a problem for California and the Southwest, but now it's all over the country.
New York mainly had a Puerto Rican problem, which is a whole other kettle of fish. On the whole, it's less bad now than it used to be.
Read Lawrence Auster's essay on immigration coupled with multi-culturalism and their combined effect on our culture. It's a long read but very prescient.
The Path to National Suicide by Lawrence Auster (1990)
An essay on multi-culturalism and immigration.
Excerpt:
How can we account for this remarkable silence? The answer, as I will try to show, is that when the Immigration Reform Act of 1965 was being considered in Congress, the demographic impact of the bill was misunderstood and downplayed by its sponsors. As a result, the subject of population change was never seriously examined. The lawmakers stated intention was that the Act should not radically transform Americas ethnic character; indeed, it was taken for granted by liberals such as Robert Kennedy that it was in the nations interest to avoid such a change. But the dramatic ethnic transformation that has actually occurred as a result of the 1965 Act has insensibly led to acceptance of that transformation in the form of a new, multicultural vision of American society. Dominating the media and the schools, ritualistically echoed by every politician, enforced in every public institution, this orthodoxy now forbids public criticism of the new path the country has taken. We are a nation of immigrants, we tell ourselves and the subject is closed. The consequences of this code of silence are bizarre. One can listen to statesmen and philosophers agonize over the multitudinous causes of our decline, and not hear a single word about the massive immigration from the Third World and the resulting social divisions. Opponents of population growth, whose crusade began in the 1960s out of a concern about the growth rate among resident Americans and its effects on the environment and the quality of life, now studiously ignore the question of immigration, which accounts for fully half of our population growth.
This curious inhibition stems, of course, from a paralyzing fear of the charge of racism. The very manner in which the issue is framedas a matter of equal rights and the blessings of diversity on one side, versus racism on the othertends to cut off all rational discourse on the subject. One can only wonder what would happen if the proponents of open immigration allowed the issue to be discussed, not as a moralistic dichotomy, but in terms of its real consequences. Instead of saying: We believe in the equal and unlimited right of all people to immigrate to the U.S. and enrich our land with their diversity, what if they said: We believe in an immigration policy which must result in a staggering increase in our population, a revolution in our culture and way of life, and the gradual submergence of our current population by Hispanic and Caribbean and Asian peoples. Such frankness would open up an honest debate between those who favor a radical change in Americas ethnic and cultural identity and those who think this nation should preserve its way of life and its predominant, European-American character. That is the actual choiceas distinct from the theoretical choice between equality and racismthat our nation faces. But the tyranny of silence has prevented the American people from freely making that choice.