Remember when Congress put the new immigration law on the books two years ago? Remember how the law, with its stiff penalties against American employers who hire illegal immigrants, was supposed to discourage Mexicans and others from crossing the border illegally in search of jobs?

Initially, it worked. For several months, illegal crossings dropped substantially. But the success didn't last long. Evidently the stiff penalties against employers weren't quite stiff enough.In any event, recent reports indicate that illegal entry of aliens across the Mexican border is increasing despite the new immigration law that was intended to stop it or at least slow it to a trickle. Specifically, Scripps Howard News Service reports, two studies - one by a Mexican college and another by the University of California - say a heavy flow has resumed. Said one California researcher:

"Clearly, we have reached the end of the period of fear, uncertainty, and confusion about the 1986 law among workers still based in Mexico. Those who delayed migration to the U.S. during 1987 are now coming, having observed that work is still available even for new arrivals lacking papers."

The California study said some employers are getting around the law by subcontracting work, accepting identification and other documents they know to be forged, and hiring workers for brief periods (less than three days), which requires no paperwork.

This suggests that authorities should get tougher on enforcement and that changes may be needed in the law. As it stands, employers are required to check papers of anyone applying for work, but they don't have to authenticate the documents. Given the advanced state of electronics in this country, it shouldn't be too difficult to design a system by which employers could quickly verify such documents as passports, registration papers and Social Security cards.

Authorities also ought to crack down hard on those who supply counterfeit papers to illegal immigrants, as well as those who shelter the aliens.

Those who defy American immigration laws can only make it in this country through the connivance of employers and residents of the United States. Congress should make it unmistakably clear that severe penalties will be exacted for such connivance.