Onyango Obama, the half brother of the president’s father, who did have a driver’s license, was taken into custody on an immigration detainer after his arrest in Framingham on Aug. 24. Immigration and Customs Enforcement released him on Sept. 8 but has refused to say why, citing federal privacy laws.

In another recent case, a Mexican immigrant was arrested on a charge of drunken driving last weekend in Boxborough, and the police said he had five previous drunken-driving convictions. The man, Eduardo A. Torres, had been deported three times previously, according to immigration officials.

On Wednesday, Mr. Moore joined three county sheriffs at a State House news conference calling for Mr. Patrick to embrace the Secure Communities program immediately. Also on Wednesday, Senator Scott Brown, a Republican facing re-election next year, urged Janet Napolitano, the homeland security secretary, to “proceed with the full activation” of the program in Massachusetts.

He also suggested that Mr. Patrick’s resistance would delay the program’s activation in Massachusetts; it currently operates only in Boston. But a spokesman for the immigration agency, which runs the program, said that would not be a factor.

The sheriffs of Bristol, Plymouth and Worcester Counties, all Republicans, said they were working with federal officials to adopt elements of the program in their counties immediately. Mr. Patrick said on Wednesday that the state already sends fingerprints of arrestees to the F.B.I., which is free to share them with immigration agents. The state also sends fingerprints of convicted criminals directly to the immigration agency once they arrive in state prisons, he said.

“This is about grandstanding and headlines,” Mr. Patrick said of his critics on the issue. “Meanwhile, the public should know that every fingerprint is sent to the federal government; they should know that every felony is referred to the federal government.”

It is far from certain that Mr. Moore’s bill will pass both houses of the legislature; similar crackdowns in recent years have passed the Senate but not the more liberal House of Representatives. But Eva Millona, executive director of the Massachusetts Immigrant and Refugee Advocacy Coalition, said she was worried.

“We seem to continue to lose supporters,” she said.

Ms. Millona added that it was unfair to connect drunken driving with illegal immigration. “Drunk driving is another issue, and people should be punished for it,” she said. “But immigration status has nothing to do with it.”