Anthony Atamanuik has at least one thing in common with Donald Trump: Each man finds himself occupying a historic office, somewhat surprisingly and under high stakes. Trump’s office has been home to every president since Taft; Atamanuik’s used to belong to Stephen Colbert. I visited in late August, when Atamanuik was still settling in. There were big windows and high ceilings with exposed rafters. There was an executive bathroom. He showed me a “WristStrong” bracelet, a relic of Colbert’s injury, that he had fished out of the rafters using a decorative saber given to him by J.D. Amato, his friend and former co-executive producer. The saber had “truth” engraved on one side of the blade and “satire” on the other.

Everything in this office seemed to emphasize the gravity of Atamanuik’s position, and he paced its expanse like a chief executive or, possibly, a prisoner. Briefly alighting behind the desk, he told me it used to support two giant computer monitors that obscured his view of the room. He had to peer over them to talk to people, either craning his neck or awkwardly hovering above his chair, but he didn’t move them for weeks, because that’s how Colbert did it.

For the last six months, it has been Atamanuik’s job to imitate Donald Trump on “The President Show,” a late-night television show on Comedy Central whose conceit is that the president hosts a late-night television show. This project asks Atamanuik to continue the legacy of past masters like Colbert and Jon Stewart even as he grapples with the most galvanizing public figure in modern memory — an easy task, so long as he manages to be really funny every week.

Atamanuik regards the pressure as an opportunity. He sat in a tubular-steel chair in front of his desk and expounded on Trump as both symptom and ailment of our current politics, periodically returning to his computer to check the occasional fact — for example, whether his home county, Suffolk County, Mass., went for Trump in November’s election. (It didn’t.) A substantial television hung on the wall, tuned to MSNBC and connected to an Xbox by trailing cables. The south side of West 54th Street crowded the window to his right; on his left, a bookcase supported one shelf of shoes and two of political hardbacks, plus big-idea best sellers and Vintage Classics with lined spines. It was the library of a pop polymath, someone who had kept his books from film school and, against trend, added to them.