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But Ms. Vaughan said the Department of Homeland Security hasn’t been proactive in pushing the visa retaliation.

A Homeland Security spokesman didn’t return a request seeking comment.

The massive immigration bill that passed the Senate this year waters down the visa penalty law, giving wide latitude to Homeland Security and the State Department to determine whether another country is being recalcitrant.

House Republicans are looking at a more concrete solution.

One of their immigration bills, which cleared the Judiciary Committee this year, would give the Homeland Security secretary the power to indefinitely order the detention of immigrants who are deemed to be public safety threats. That bill could come to the House floor this year if Republicans move ahead with an immigration debate.

The bill mirrors an approach championed by Rep. Lamar Smith, Texas Republican, in the previous Congress.

Ms. Rabinovitz at the ACLU said giving ICE permanent detention powers could be unconstitutional and is certainly misguided. She said the agency should be trying to figure out ways to reduce the population of detainees.

“It’s just stupid,” she said. “We’re talking about a situation where we’re spending so much money on detention, we’re in a period of fiscal straits where we should be concerned about spending our money. To lock up people who aren’t a flight risk doesn’t make sense. All we’re saying is provide them with a bond hearing.”