“I can’t,” he says, searching for a response to Letterman’s comments. “I’m too embarrassed to repeat that myself.” Then Mulaney describes it as “if you could imagine him to say anything you’d ever want, what would it be?”

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The likable and self-deprecating 35-year-old comic does stand poised to take the mantle Letterman described. In three years, he’s released a critically acclaimed stand-up special, offered a beloved portrayal of a crotchety old man opposite Nick Kroll in “Oh, Hello on Broadway” (filmed for Netflix) and is now on his “Kid Gorgeous” stand-up tour, selling out massive venues such as DAR Constitution Hall this Friday through Sunday. And all those hits follow his biggest career failure: “Mulaney,” his poorly-reviewed 2014 Fox sitcom, that went off the air after just 13 episodes.

Mulaney created and starred in the semi-autobiographical show about a comedian and his roommates in New York. He took a risk with the now-rare multi-camera, live-studio audience approach, which he liked from his “Saturday Night Live” writing days.

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“I don’t like to say I’m glad it didn’t work because a lot of people lose a job,” Mulaney says, and pauses. “But I’m glad it didn’t work. It was like, the best thing that ever happened.”

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He recalls, in the middle of production, driving home and his heart almost stopping at the thought of making a full 22-episode season.

“I take full responsibility for the funny jokes and for the stuff everyone hated. It was so enervating,” he said. Running a sitcom like that is “just not, for me, the best mind-set to be in to be the funniest possible.” Mulaney would find that mind-set when starting “Oh, Hello” in a downtown theater and not caring whether it bombed at all.

Getting your own network sitcom once was the pinnacle of success for a stand-up comic. But now, with streaming services, social media and a limitless Internet, doubling down on what you find intuitively funny — even if it’s two young guys playing septuagenarians obsessed with tuna sandwiches — can get you a devoted following, along with critical acclaim.

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“It’s always better when you do your thing, and make people come to you,” Mulaney says. “You can only meet the audience halfway. If you’re trying to meet them 70 percent of the way, and begging for 30, you’re going to be seen as desperate.”

As soon as “Mulaney” was canceled, he hit the road, eventually filming “Comeback Kid.” The 2015 Emmy-nominated special explored the typical markers of adulthood, such as marriage and house-hunting (“This is an on-fire garbage can,” his real estate agent would say. “Could be a nursery.”)

A month later, Mulaney was playing George St. Geegland to Nick Kroll’s Gil Faizon. The pair of self-involved Upper Westsiders got a cult following in regular sketches on Kroll’s TV show and eventually moved to an “Oh, Hello” stage show, in which they spoofed old-fashioned showbiz tropes, pranked guests such as Steve Martin and Chris Pratt and sprinkled in hilariously odd pronunciations (“cocaine” became “cuh-cane.”)

Kroll and Mulaney met when Kroll, then a Georgetown senior, cast Mulaney, a freshman, in the university’s improv troupe.

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“Honestly when I met him, I was like, this guy’s so funny, I’m going to hold on tight. I’ve sufficiently done that for a long time,” Kroll says.

Mulaney spent a college summer sleeping on Kroll’s couch in New York while interning at Comedy Central and hitting open mics at night. After graduating with an English degree, Mulaney headed back to New York to make a real go of a career in comedy, working as an assistant at Comedy Central and performing stand-up at night. He also toured with another college buddy, Mike Birbiglia, for 30-show runs in 30 days.

“Not just doing stand-up in New York was very, very key, and Mike’s really to credit for all that,” Mulaney says.

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Doing spots on VH1’s “Best Week Ever” taught him how to write topical jokes for TV. At 25, SNL hired him as a writer. “I don’t know how I’m ever going to do this,” he recalled feeling. “But, a lot of it was the same skill set. Just now you’re in the fancy building on the high floor.”

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He was with SNL for six years, becoming a celebrated writer and helping co-create the popular Stefon character, played by Bill Hader.

Then the sitcom, executive produced by Lorne Michaels, came along. When it failed, Mulaney remembers Kroll saying “I’m sorry, but it’s really funny how much your show bombed.” Mulaney describes himself a “little achiever” — the kind of guy who gets to the office early — and could see the inherent humor to it. Up until then, almost everything he had worked at had done very well.

“Narratively speaking, it’s a funny thing to happen to a character,” Kroll says. “It happening to my incredibly dear friend, after seeing how hard he worked on it, was terrible, but also watching him bounce back from it was an amazing testament to how strong of a guy he is and how deeply funny he is. One show doesn’t make or break a career or life unless you let it.”

With hindsight, Mulaney says it was also good to have the experience of “eww, people don’t like this” and to “read some of the worst things people could say.” When he’d say to his wife, “this is so weird,” she’d respond: “You were never bullied. Welcome to what a lot of us went through. … You’ve never been mocked, you know, this is what it’s like.’ ”

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These days, Mulaney also voices for Kroll’s animated Netflix show about puberty, “Big Mouth,” and writes episodes of “Documentary Now!” for Hader and Fred Armisen.

As for stand-up, Mulaney still tells personal stories, in a funhouse mirror kind of way: “People are always 13 feet tall in my stories, because that’s how they feel to me,” he explains. And while he hasn’t shed his polite persona, he’s tapped into a grumpier energy. “I’m more comfortable yelling at things. The Broadway show opened that up a lot.”

“I’m not a trained actor. I was uncomfortable from the very, very beginning off-Broadway playing such a terrible guy, who I also had an affection for,” he adds. “But something about doing that night after night and sometimes really alienating the audience was fun.”

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On Friday, he’ll return to DAR Constitution, where as a college student he saw jazz musician Dave Brubeck perform.

“I remember he said, ‘By the way, I have my 73rd album coming out next week. So it’s a real eh-vent,’” Mulaney says. It’s a bit of inspiration he carried with him to “Oh, Hello,” where he used the line often: “It’s a real eh-vent.”