The intentions of the law which President Bill Clinton signed before the November election are plain enough - to curb the number of legal immigrants, prevent abuse of the political asylum grounds for entry into the country, and above all to impose the toughest clampdown in decades on an illegal immigration reckoned to be running at almost 300,000 a year.
Some 60,000 to 70,000 illegal immigrants are caught and deported each year by the authorities, but under the new laws that total should rise considerably. Henceforth, anyone whose visa is found to have expired must return home to apply for a new one, while people who have overstayed by more than six months will be barred from returning for between 3 and 10 years.
In addition, some 1,500 more border guards have been taken on by the Immigration and Naturalisation Service (INS), in a probably vain attempt to staunch the flow of immigrants who slip into the US withoutpapers - mainly across the southern border with Mexico, but also from Caribbean countries like Haiti, or crammed in a boat bound from China or south-east Asia.
But almost every proviso of the measure has caused at least as many problems as it solves. Civil-rights lawyers and immigrants' rights groups have gone to court to challenge the new powers of officials to interview asylum- seekers at the border and to summarily turn them back if they are unsatisfied the claim is genuine. "On the basis of a snap judgement, people may be sent home, possibly to face torture or death," Robert Rubin, a civil-rights lawyer told a Washington judge this week, in a vain effort to delay implementation of the law.
For most, however, of the estimated 5 million illegal immigrants here - some 2 million of them on overstayed visas - the real fear is of losing their livelihood and of being deported. In the belief that they would be sent home if they did not submit applications for residence by 1 April, thousands of people queued at INS offices in the days before the supposed deadline, desperate to regularise their status or that of relatives.
In fact the real cut-off date may only come in six months, with closure of the so-called "pay-to-stay" loophole that allows illegal immigrants to pay a $1,000 (pounds 625) fine and stay in the US while their residence applications are being processed. This can take years. But unless Congress votes an extension, pay-to-stay will stop on 30 September, raising, in theory at least, the spectre of round-ups and mass deportations.
Almost certainly, however, it will not come to that. Mr Clinton accepted the Republican-driven measure to shore up his support in the political centre, and especially in the four electoral college "mega-states" of Texas, California, Florida and New York, where more than half all immigrants, legal and illegal, live. But without the immigrants, whole sectors of the local economy would founder.
At the 1996 Republican Convention in San Diego, a few miles north of the Mexican border, speaker after speaker rattled off a xenophobic anti-immigrant litany, railing against overwhelmed state schools and welfare services, and cut-price labour that was depriving deserving Americans of jobs. But a quick check revealed that many of the cleaners and other menial workers who kept the convention running were ... illegal immigrants.