The family of Geraldo Lunas Campos said a witness saw him choked by guards in an El Paso detention facility this month. Federal officials said he died by suicide.
Republicans asked the justices to step in after a federal court rejected their claims that the state's new congressional map violated the Constitution.
The actions signal a breaking point for the federal bench in the Eastern District of Virginia after Lindsey Halligan was disqualified as U.S. attorney there.