"Fast forward to today, I'll be on a call … with some U.S. attorneys who are deciding where to arraign somebody who's been indicted for death threats against me and my family. ... That one is from the right, but there are some on the left as well," Flake said at a political forum being hosted by CNN.

Flake didn't specify which individual has made threats against him and his family. But The Associated Press reported last week that James Dean Blevins had been indicted in Arizona for threats made against "United States Senator J.F."