Mr. Clinton joined Mr. Spacey onstage, and a bromance between the two men ensued. Mr. Clinton grinned widely, relishing the impersonation. He put his arm around Mr. Spacey.

It was only the latest public display of affection between an actor, who is currently best known for portraying one of the most morally bankrupt presidents ever to come out of Hollywood, and a former president, who ever since he played the saxophone on “The Arsenio Hall Show” in 1992, has had a special bond with the small screen.

Mr. Spacey, a Democratic donor, first met Mr. Clinton in the White House during his first term. In two industries — politics and entertainment — known for fleeting friendships of convenience, the men seemed to genuinely bond. They stayed in touch and grew closer in Mr. Clinton’s post-presidency, talking a couple times a month and collaborating often on philanthropic work. It’s a relationship that is well known to those close to Mr. Clinton and that has become evident since I began covering him and his wife, Hillary Rodham Clinton. If you look closely at the décor in Underwood’s office on “House of Cards,” you’ll see a photo of Mr. Spacey and Mr. Clinton at dinner together plugging away on their BlackBerrys. The photo is likely to move to the White House with President Underwood in Season 3, which will begin streaming on Netflix on Feb. 27.

Of all the TV shows for Mr. Clinton to be associated with as Mrs. Clinton prepares for a 2016 presidential campaign, the coldly cynical depiction of Washington in “House of Cards” might not be the best for political optics.