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“Our office has always collected I-9 forms and legal documentation for all employees at the time they were hired and also has resolved the issue with E-Verify,” said Webb spokesman Will Jenkins.

Part of the problem is that it’s unclear who should be enforcing the law in the Senate.

Some pointed the finger at the Senate Rules and Administration Committee, which oversees operations for the upper chamber.

But Senate officials say each congressional office is similar to an independent business and is responsible for its own internal operations. The Senate nevertheless makes extensive efforts to make sure member offices are aware of the rules, including offering repeated training and a tutorial to talk office managers through the process, and giving frequent reminders that E-Verify is required.

The law itself gives some guidance, charging the Justice Department with enforcement. Justice officials, however, say responsibility is divided between U.S. Immigration and Customs Enforcement, which is part of the Department of Homeland Security and brings the cases, and the Executive Office for Immigration Review, which adjudicates cases.

It was unclear whether any individual E-Verify malfeasance cases have been brought.

In the House, unlike the Senate it’s difficultto get a sense for how scrupulous House members are in signing up to use E-Verify. Several hundred offices are registered, but the House also offers a centralized service to run checks through the system, and many members make use of that service.

The bill advancing through the House to make E-Verify mandatory is sponsored by Judiciary Committee Chairman Lamar Smith, Texas Republican. It passed his committee on a party-line vote last month.

A similar bill has been submitted in the Senate. It is sponsored by Sen. Chuck Grassley, Iowa Republican, and co-sponsored by 10 senators, including Mr. Boozman.

No action has been taken on that legislation. In fact, Sen. Charles E. Schumer, New York Democrat and chairman of the SenateJudiciary Committee’s immigration panel, held a hearing aimed at poking holes in the effectiveness of a mandatory E-Verify law.

Nationwide, USCIS said nearly 300,000 employers were registered to use the program as of Oct. 15. The agency recorded more than 796,000 queries from Oct. 1 through Oct. 15 this year.