''We have lost control of our own borders.''
So declared Attorney General William French Smith in June 1981, as he recommended the most sweeping revision of American immigration law in 30 years. The Senate Aug. 17 passed such a bill overwhelmingly, 81 to 18, and a similar bill waits in the House Judiciary Committee. Whether Congress finally acts on a measure urged by President Reagan remains to be seen.
Half a million illegal immigrants enter the nation annually, according to some estimates, in addition to legal immigration quotas believed to be the most generous in the world.
The Senate bill would seek to regulate a situation where estimates of illegal aliens in the country range from 3 million to 6 million, where border patrols are hard pressed, and where domestic unemployment is 9.8 percent. The last major immigration act (McCarran-Walter bill) was passed in 1952 and established quotas. The pending bill, sponsored by Sen. Alan K. Simpson (R) of Wyoming and Rep. Romano L. Mazzoli (D) of Kentucky, makes some radical departures from current legislation. The new law would:
* Impose civil and criminal sanctions against employers who knowingly hire illegal aliens. (Lawmakers hope to reduce illegal entry by diminishing the incentive of quick jobs.) Employers of less than four people would not have to make reports.
* Set up an elaborate verification program to help employers determine the legality of potential workers. The program may include hard-to-forge identification papers printed on bank note paper like dollar bills.
* Provide amnesty for most illegal aliens already in the United States, with terms varying by category and length of stay.
* Revise temporary guest-worker programs to help US areas hit by worker shortage, such as harvesters for special farm crops.
* Put a cap on overall alien admissions to the US at 425,000 (about the present level) with quotas of 20,000 migrants from each foreign country. The exceptions are Mexico and Canada, which each would have a quota of 40,000. Canada's unused quota, if any, would be available to Mexico.
* Revise restrictions on categories of those allowed to immigrate: special treatment for brothers and sisters of American citizens (known as the fifth visa preference) would be eliminated.
* Streamline procedures for exclusion, deportation, and refugee claims.
Until recently, Congress has avoided a problem that is admittedly changing America's demography. A witness at a Brookings Institution seminar last December noted that ''there are 2,300 Border Patrol agents and at any given time there are only about 230 on the line.'' Reporting for the President's Select Commission on Immigration in March 1981, chairman Theodore M. Hesburgh acknowledged ''dissatisfaction among US citizens with an immigration policy that seems to be out of control.''
The task force estimated that 500,000 people might be added to the permanent population each year through illegal immigration, while other illegals make a circular flow annually across borders.
In introducing the bill to Congress, Senator Simpson said its purpose is ''to bring immigration to the United States back under the control of the American people.'' An unusual coalition voted against the bill; some thought it too permissive, others thought it too harsh. Sens. Edward M. Kennedy (D) of Massachusetts and Gary Hart (D) of Colorado wanted more lenient terms. Sens. Jesse Helms (R) of North Carolina and John Tower (R) of Texas wanted sharper action.
The House now determines the fate of the bill. Rep. Peter W. Rodino Jr. (D) of New Jersey, who heads the House Judiciary Committee, says the bill will come up in committee in September. The House has a nearly identical bill pending in the immigration subcommittee.