CAN A FOOLPROOF identification card be developed in this country at this time? The short answer is "no," and that has large implications for many areas of public policy. For instance, a Cabinet task force on illegal immigration has apparently been unable to find an easy ID system to enable employers to identify illegal aliens. And this week, Chicago election officials told a House panel that because existing IDs are unreliable, the administration's plan for election-day voter registration would be likely to produce massive fraud.

As if to illustrate the problem, a Baltimore grand jury last week indicted one Leon R. Collier, also known as Robert E. Lee Pugh Jr., on charges of prescribing drugs illegally and impersonating a physician at, of all places, the Maryland Penitentiary Diagnostic Center. When the state police arrested Mr. Collier-Pugh, they found in his car a "mound" of tax returns, federal and state drug-dispensing licenses and other documents that suggest the man may have used at least 19 identities.

The Collier-Pugh case is one example of the booming traffic in phony IDs among swindlers, tax evaders, fugitives from justice, drug dealers and welfare cheaters -- as well as illegal aliens and unlawful voters. A Justice Department committee estimated last year that crimes involving faked identities now cost society more than $10 billion per year.

Such frauds are not easy to stop, as Labor Secretary Ray Marshall has learned while looking for a way to curb employment of illegal aliens. Mr. Marshall first proposed that the Social Security card be made counterfeit-proof and used as a "work card" for citizens and legal aliens. That approach raises substantial civilliberties concerns. Even if those could be resolved, a national "work card" would not work because it would not be reliable. False identities could still be built, as they are now, by getting a birth certificate in someone else's name -- often somebody who died young -- and using that document to obtain a driver's license, bank accounts and -- yes -- a Social Security card. And if the card were counterfeit-proof, the fake identity would seem all the more genuine.

Congress can discourage some of this by tightening the laws against interstate trafficking in fraudulent documents. The administration ought to crack down on those who use phony papers to get federal benefits. As the Justice Department panel concluded, however, the best preventive measures are coordination of birth and death records and strict controls on access to birth certificates and driver's licenses. Responsibility for those steps rests and should remain with the states. Tightening up every state's record-keeping sufficiently will take some time. Meanwhile, it would be rash to launch any new government program that depends too much on any single ID to prove who's who.