THE GOVERNMENT'S first comprehensive study of illegal immigration confirms that the flow is large and growing - "several million" annually against a legal flow of 400,000 - and that it cannot be limited unless very difficult political and social choices are made. A Soviet-style Iron Curtain would facilitate border policing, for instance, but few Americans would tolerate it. Police sweeps in neighborhoods where many illegals live would net large hauls, but this tactic would be disrupting and undiscriminating. Little can or should be done about most of the illegals already here, the new report declares.

Nor, to judge by Congress' demonstrated hesitancy, are Americans yet ready even to hold employers responsible, civilly or criminally, for hiring illegals: This is one suggested method of control. Such a law would shift a difficult burden of law enforcement away from the enforcement agencies and push the country toward a system of national identity cards that civil libertarians and others recognize as a sharp break with the American tradition. This is not to say that no police or legislative steps can be taken. But they must be taken carefully and with an awareness of limitations and costs.

As the inter-agency Domestic Council committee (headed by former Attorney General Edward Levi) clarifies in its 257-page report, the problem goes not only to the nature of America but the nature of the world. It is the "push" of unemployment in various lands, particularly Mexico, that energizes emigration. The solutions - labor-intensive development, population control - are obviously long-term. It is the "pull" of the American economy and the promise of opportunity that energizes immigration, legal as well as illegal.

The United States could end the illegal flow at a stroke by removing all barriers on legal immigration. But that is out of the question. The country is left to consider just what mix of immigrants it wants: how many, of what family relationships or countries of origin, of what skills. It is the disparity between the push-pull factors that operate on their own, and the choices of immigration policy that do not get made unless the country deliberately makes them, that defines the problem now.

Even as the United States celebrates itself as a nation of immigrants, of course, it imposes sharp restrictions. These restrictions have been variously adjusted in recent decades, but few people would claim that the ones in effect today serve society particularly well. In theory, the foreign relatives of Americans have special access, but the last Congress carelessly cut the number of Mexican relatives eligible to come. Historically, a concern for the effect on the labor market has been central to immigration restrictions, but the American hires and competitors of illegal migrant labor, especially unskilled labor, are sharply divided on this point now. The Hispanic community sees the restrictions as particularly burdensome, not to say discriminatory.

The Ford administration, though it produced this excellent report, did not have the time or political energy to act upon it. The Carter administration surely does. Secretary of Labour Ray Marshall, moreover, brings particular expertise to this problem. Since immigrants, legal and illegal, fall mostly into the Democratic constituency, the new administration has a special license, and a special responsibility, to act.