Danes told NBC's "Today" show that her reaction was a simple "what?!"
when she heard the president liked the new Showtime series.
"It's amazing. An amazing honor," Danes said. "He's in the opening credits, so maybe that's why!"
Obama appears in the show's title sequence voicing a line from a speech he made following the death of Osama Bin Laden: "We must, and we will, remain vigilant at home and abroad." The show's title sequence also includes a clip of Bill Clinton discussing terrorism.
In the show, which is set in Washington, D.C., Danes plays a CIA officer investigating a Marine previously held captive by al Qaeda.
Obama revealed that he watches the show in an interview with "People" magazine this week, also listing HBO's "Boardwalk Empire." He admitted that his TV tastes are "a little darker" than those of his wife and daughters, who only join him in viewing "Modern Family."