Mr. Feigin said the court should limit the law to narrow circumstances that would exclude many of the scenarios that troubled the justices. The defendant, he said, must want to bring about the result of inducing the immigrant to come or stay; the immigrant must understand what was going on; and the defendant must be a substantial participant in the effort.

Mark C. Fleming, a lawyer for the defendant, Evelyn Sineneng-Smith, said the government’s proposal would amount to wholesale and improper revision of the federal statute, one he said currently applies to teachers, pastors, doctors and lawyers.

Ms. Sineneng-Smith ran an immigration consulting firm in San Jose, Calif. Her clients, mostly from the Philippines, worked without authorization in the home health care industry. Ms. Sineneng-Smith offered to help them get green cards under a Labor Department certification program that she said would give them permanent resident status and allow them to work legally.

But the program had expired. Ms. Sineneng-Smith nonetheless charged her clients $6,800 to file applications she knew to be futile. She was convicted of mail fraud, a conviction she did not challenge in the Supreme Court, and of violating the 1986 law.

Justice Elena Kagan asked whether there had been prosecutions of more sympathetic defendants of the sort her colleagues had been asking about. Mr. Fleming had one example.

In 2012, a Massachusetts woman, Lorraine Henderson, was convicted of hiring an unauthorized immigrant to clean her home and of offering general and not always reliable advice about immigration law.

In that case, Judge Douglas P. Woodlock, of the Federal District Court in Boston, wrote that the “plain and unadorned language” of the law “can be read to cast a wide net over those who interact with illegal aliens by offering employment.”