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On the video, Michigan Rep. Peter Hoekstra of Michigan, ranking Republican on the House Intelligence Committee, says, “The real question we now face is, What is President Obama’s strategy to confront this threat from radical jihadists?”

About 100,000 viewers had visited the video Web site as of Monday, according to Mr. Boehner’s office.

On the Senate floor Monday, Mr. McConnell said the appropriate time for Congress to debate closing the prison camp is after “the administration has a plan to safely detain, prosecute, or transfer these detainees.”

“With no safe alternative, this is the only sensible approach,” he said.

The Defense Department has confirmed that 18 former detainees had returned to the battlefield and at least 40 more are suspected of having rejoined terrorist networks after being released from Guantanamo.