Five and a half years into his presidency, Mr. Obama has had a powerful impact on the nation’s popular culture. But what many screenwriters, novelists and visual artists have seized on is not an inspirational story of the first black president. Instead they have found more compelling story lines in the bleaker, morally fraught parts of Mr. Obama’s legacy.

“We were trying to find a bridge to the same sort of questions that Barack Obama has to address,” said Joe Russo, who with his brother, Anthony, directed “Captain America: The Winter Soldier.” “If you’re saying with a drone strike, we can eradicate an enemy of the state, what if you say with 100 drone strikes, we can eradicate 100? With 1,000, we can eradicate 1,000? At what point do you stop?”

Beyond “Captain America,” a virtual arts festival of films, books, plays, comics, television shows and paintings have been using as their underlying narratives the sometimes grim reality of Mr. Obama’s presidency.

The commando raid that Mr. Obama ordered to kill Osama bin Laden is the basis for the actions of the fictional President Ogden in the Godzilla comic books.