Alec Baldwin may have won an Emmy for his portrayal of President Trump on “Saturday Night Live,” but Anthony Atamanuik is doing an impression of the former reality TV star turned leader of the free world that’s even more cutting — and perhaps more dead-on.

Each week, on Comedy Central’s late-night “The President Show,” Atamanuik portrays the commander-in-chief as a childish lout driven entirely by ego and a hunger for self-satisfaction. If Atamanuik’s Trump sees a big truck on the street, he yells at the driver to honk the horn. If he finds a couple of hamburgers, he devours them. He holds forth as the nation’s newest late-night host, broadcsating from the Oval Office and Mar-a-Lago with Vice President Mike Pence as his sidekick. You might say it’s a funhouse mirror of F.D.R.’s famous fireside chats.  “Let’s roll!” Atamanuik yells each week to open the show.

It’s not the least bit flattering. But it is extremely funny.

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In the past, late-night hosts like Johnny Carson would hide their political views. But Atamanuik wears his on his sleeve. “What Charlie Chaplin did really affected the image of Hitler,” he says, referring to the comic actor’s 1940 turn in the famous satire “The Great Dictator.”

Atamanuik’s modern-day POTUS portrayal deprives Trump “of what his machismo is, and all the bullshit he’s selling,” notes the comic as he talks about “The President Show” over an egg-salad-and-bacon sandwich and a chocolate egg cream at Eisenberg’s Sandwich Shop in Midtown Manhattan. “By replacing [that machismo] with reason and liberal thinking and a lot of buffoonery — by Homer Simpson-izing him — I think you rob him of his power.”

The show injects an element of the surreal into the nation’s late-night antics. Most of the wee-hours hosts tell jokes, put on sketches, test out pranks, or deliver ersatz news broadcasts that often tell viewers more than their real-life counterparts. But “The President Show” is just, well, off the beaten path. Here’s a veteran of New York’s improv clubs eagerly channeling a figure who many people find unbelievable. In one recent sketch, Atamanuik’s Trump was forced to learn etiquette at a charm school. But he ended up staring at himself in the mirror. ““I hate the man in the mirror,” the fake President says. “He knows my secrets.” It’s quite different from making jokes about Trump in a monologue.

Each episode mines humor from current events. Atamanuik’s Trump isn’t afraid to step out of his gilded penthouse and into the streets. The “president” interviews “guests” who in many cases are activists or celebrities who have publicly scorned the real White House occupant. He treats each guest as if they are one of the students he has taught comedy stylings to over the years. He likes the guests to meet him in costume, and learn they can have a playful back and forth, even if their attitude toward the real Trump is less munificent. “If you had a chance to sit with the president how would you do it? You know I’m not going to kick you out. What would you do?”  Atamanuik performs most of the show and its field pieces live, without stopping for retakes.

Comedy Central is betting on the show to take things even further. Since the program debuted in April, the Viacom-owned cable outlet has twice extended its run. Now Atamanuik has grand plans for what might be the most surreal series in TV’s highly competitive late-night arena.

“We are looking for our Jeff Sessions right now,” confides the host. Over the course of the show, Atamanuik has built a kitchen cabinet of Trump associates. Peter Grosz, one of the executive producers, plays Pence. But the show also has a Steve Bannon (John Gemberling), a Donald Trump Jr. (Adam Pally) and an Anthony Scaramucci (Mario Cantone).

Atamanuik has been aping Trump for only a little while, but he’s been part of the New York improv scene for years. In fact, he stumbled on Trump; someone asked for it during a show. The rest has developed from studying the president’s cadences and tics and the way he moves physically to accentuate ideas.

The impersonation has sparked genuine reactions. One day, when Atamanuik was walking around Times Square in character to tape a segment, a woman in a minivan started shouting profanities at him. “She almost ran her car into the sidewalk, she was so angry,” Atamanuik recalls.

Even though the program airs once a week for 30 minutes, Atamanuik says he works just as hard as his late-night contemporaries. “There is no luxury in what we do. It is, I would argue, probably more difficult than what ‘Saturday Night Live’ does,” he says. “We have to fill 21 minutes and 15 seconds, and it has to be relevant and interesting, with one of the most despicable characters on the landscape today.” What if the President does something worthy of praise? “It would be like Cesar Milan: If he does something good, I would give him a treat,” says Atamanuik. “But he’s still a dog. That’s my answer to that.”

Should the President run afoul of Congress or the law, Atamanuik still thinks his show will have traction. “We could do a last season of him in jail, or just post-presidency to wrap up,” he suggests. Besides, he’s hoping for a longer run than Trump’s — he’d like the concept to prove winning enough that Comedy Central will want the show to continue when there’s a different leader in the White House.