AT THIS POINT, only the president himself can rescue the critical component of his own Cabinet task force's package of immigration policies -- a new and less easily forged Social Security card, now threatened with extinction by sudden assault from a few powerful but misguided administration snipers.

Most people who have studied the immigration problem, including a majority of the Select Commission on Immigration and Refugee Policy (whose final report formed the basis for the task force's deliberations), subscribe to the following common sense syllogism: without enforcing strictly our existing immigration laws (or their successors), we cannot curb effectively the flood of illegal immigrants now entering the country. But without relying on some fair, accurate and simple means of distinguishing legal migrants from the illegals, proper enforcement of immigration laws becomes hopeless. Therefore, the test of any administration's determination to confront the problem seriously becomes a willingness to devise some national identifier, the most commonly mentioned being a counterfeit-resistant Social Security card.

Not only did most members of the select commission support the use of a universal identifier but, initially, the Cabinet task force also endorsed that plan. Most published accounts agree, however, that the full Cabinet rejected the proposal at the urging of a few opponents who led the attack determined to wipe out completely the concept of an identity card. Apparently First Amendment fastidiousness was less the issue than the potential use of a reliable Social Security card to impose sanctions on employers -- among them the giant agribusinesses of the western states -- who often hire illegal migrants.

The president has been badly served by his Cabinet in this instance, though not by its task force on immigration. That group recognized in its scrutiny of the immigration tangle something long obvious to experts such as Sen. Alan R. Simpson (R-Wyo.), formerly an influential member of the Select Commission and now chairman of the Senate Judiciary subcommittee on the problem -- namely, that the cosmetic substitute or requiring workers and employers merely to sign a piece of paper attesting to the employee's legal status is meaningless.

At a time of continuing high unemployment among low-income workers in this country, both native-born and immigrant, asking illegals to swear pro forma to their legality while employers wink at the process reduces the level of national cynicism about hiring underpaid illegals to a new low point. Sen. Simpson said as much the other day, while urging that some form of national identifier, a new Social Security card or a useable alternative, be enacted.

Mr. Reagan should wupport the original Cabinet task force recommendation for a Social Security identifier. Undoubtedly creating a national identity card will make it easier to penalize unscrupulous employers who violate the immigration laws. That, however, seems a worthwhile step for a president committed already to a range of experimental programs in the field, including the new Mexican "guest worker" scheme and the elaborate plan to legalize the status of millions of undocumented workers already living in the United States.