“I wish things were that ruthlessly efficient,” Mr. Obama was overheard saying to Reed Hastings, the Netflix C.E.O., who invited the president to do a cameo on the show. Mr. Obama joked of the sleazy, congressman-murderer Mr. Underwood, “This guy’s getting a lot of stuff done.”

It may be a fool’s errand to psychoanalyze anyone — let alone a sitting president — based only on the books he reads or the music he listens to, or the television shows he watches.

Since leaving office, Bill Clinton has said he liked “24,” Fox’s terrorism cliffhanger, and — you guessed it — ABC’s “Scandal,” a political thriller set in Washington. Ronald Reagan, a former actor, once offered to appear on his favorite show, the sitcom “Family Ties.” (His offer was rejected.) Franklin Roosevelt was said to like Mickey Mouse cartoons in an era long before cable made TV edgy. George W. Bush was said to not be a particular fan of television, but made exceptions for A&E’s “Biography” and a variety of sports programs.

But for Mr. Obama, “Breaking Bad” and “House of Cards” are hardly the exceptions to what has become a clear pattern. Mr. Obama is also a devotee of Showtime’s “Homeland,” which offers an eerily familiar mirror to the president’s own foreign policy adventures: terrorism, Iranian nuclear negotiations, drone strikes, and an intelligence agency struggling for legitimacy with Congress and the American people.