WASHINGTON -- In another sign of Democratic unease with President Barack Obama's plans to close the Guantanamo Bay prison, the Senate Wednesday evening approved 92-3 a Republican amendment requiring the administration to provide Congress with a "threat assessment" of each detainee, describing the likelihood the inmate would rejoin a terrorist group if released and what efforts Al Qaeda might make to recruit him.

The overwhelming vote came despite an impassioned speech by Sen. Dick Durbin (D., Ill.), the second-ranking Democrat,...