The barrage was the latest salvo in an ongoing feud — alternatingly confrontational and oblique, cheeky and serious — that has smoldered since Election Day 2016, when one of them won the popular vote while the other won the electoral college and, with it, the presidency.

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In addition to her pointed jibes on CBS, Clinton — a former first lady, senator from New York, secretary of state and 2016 Democratic presidential nominee — has assailed Trump on Twitter, in speeches and even in People magazine. She has mocked him — reading a snippet of special counsel Robert S. Mueller III’s report in the president’s muggy Queens baritone — and chided him, calling for an impeachment inquiry.

The president, for his part, has seemed similarly fixated. Since taking office, he has called her “Crooked Hillary” on Twitter 127 times, led his frenzied rally crowds in chants of “Lock her up!” and is presiding over a reinvigorated investigation into more than 100 current and former State Department officials who sent messages to Clinton’s private email address when she was secretary of state.

Nearly three years after Election Day, they just can’t seem to quit each other. Like Looney Tunes’s Wile E. Coyote and Road Runner, the duo appear trapped in a disjointed call-and-response — circling, talking past and attacking each other as if the 2016 contest never quite ended.

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“Part of the reason they’re locked into this dynamic is because like any good media narrative, it requires a foe and a hero, or a foil,” said Angelo Carusone, president of Media Matters for America, a liberal media watchdog group. “It’s just Narrative 101.”

Through a spokesman, Clinton declined a request for an interview, and the White House did not respond to requests for an interview.

Current and former aides to both accuse the other of strikingly similar pathologies — being a sore loser (or, in his case, winner); harboring an unhealthy fixation on their former rival; and re-litigating the battles of the past rather than gracefully forging ahead into the future.

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To hear the Clinton folks tell it, her attacks are largely substantive and focused on news and policy, while his are frivolous and based on personality. They say Trump simply can’t get over losing the popular vote to Clinton and is haunted by this reality, which he fears undermines the legitimacy of his presidency.

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“We have a president who is irrationally and sometimes inexplicably focused on his opponent from three years ago, when he’s a lot closer to having another opponent in 10 months’ time,” said Nick Merrill, a senior adviser to Clinton who was her traveling spokesman in 2016. “He’s a small person, number one, and he clearly is smarting because at the end of the day, he knows he won the electoral college but more people who went to the polls on Nov. 8 wanted her to be president.”

They add that Clinton is not so much picking a fight as defending herself, and weighing in on critical issues of national importance.

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“She engages him like a plumber engages a clogged toilet: only when necessary,” Philippe Reines, a longtime Clinton adviser, quipped in a text message.

Christina Reynolds, a Clinton 2016 spokeswoman, said that the former Democratic nominee “is commenting in a forward-looking way” while Trump “is commenting in a backward-looking way” — a differentiation echoed by several Clinton allies.

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“Most of what she’s doing is taking a stand on things that are happening right now that go against her values, that are worthy of standing up for, and I think she is a vital voice as part of that,” Reynolds said.

In a September speech at George Washington University, for example, Clinton accused Trump and Senate Majority Leader Mitch McConnell (R-Ky.) of “abdicating their responsibility” on election security.

Trump supporters, meanwhile, fault Clinton, saying that she simply can’t move past her election loss and is not handling her defeat graciously. Kellyanne Conway, counselor to the president, pointed to Trump’s comments shortly after his victory as evidence that he tried to set a friendly tone.

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At his inaugural luncheon at the Capitol, Trump said he was “honored” that Clinton and her husband, President Bill Clinton, had attended and urged them to stand up to receive an ovation. “Honestly, there’s nothing more I can say because I have a lot of respect for those two people, so thank you both for being here,” Trump said at the time.

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But, by Conway’s telling, Clinton did not reciprocate Trump’s benevolent gesture. “Hillary engages with the president to stay relevant,” she said. “It’s unbecoming of a former presidential candidate, U.S. senator and secretary of state, but it seems to be her only release.”

Cliff Sims, a former White House aide, shared a video of Clinton’s CBS interview on Twitter and asked, “Is it not destructive to our democracy for the sore loser of a national election to say — with no justification whatsoever — that her opponent’s victory was illegitimate?”

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Clinton allies, however, say that she is almost compelled to respond to the president’s attacks on her. Yes, there are other failed presidential nominees who slinked more solidly into quiet obscurity — now-Sen. Mitt Romney (R-Utah) in the immediate wake of the 2012 election, and Democrats John F. Kerry and Al Gore after their respective 2004 and 2000 losses. But these are unprecedented times, they say, and a norm-shattering leader such as Trump demands a countervailing force.

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“Setting aside 2016, she was our secretary of state; she’s been a presidential candidate,” said Karen Finney, a spokeswoman for Clinton’s 2016 campaign. “Frankly in this moment in international politics, she has a really important and valuable perspective.”

Clinton told MSNBC’s Rachel Maddow in May that “I’m living rent free inside of Donald Trump’s brain” — a perch she seems to relish at times.

At a recent art exhibit in Venice, for example, Clinton sat at a replica of the Oval Office’s Resolute Desk and, for about an hour, read through a stack of her deleted emails.

For Trump, continuing to lace into his former electoral foe serves several purposes. People close to him say there is a certain nostalgia in the attacks for a president who enjoys reliving his 2016 victory — the ultimate flouting of the political elites he so resents. More importantly, the broadsides also motivate base voters who view Clinton as the ultimate enemy.

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Media Matters calculated that Fox News host and Trump ally Sean Hannity mentioned Clinton in 86 percent of his show’s episodes between Trump’s inauguration and the end of August. Over the past year, the group found, Trump has mentioned Clinton at least 149 times in tweets, speeches, interviews and news conferences.

“There is at least a political benefit for the president to bring up Clinton because to this day it fires up the conservative base,” said Andy Surabian, a former White House aide. “The Clintons have been enemy number one to Republicans and conservatives for almost 30 years now, so just because she lost in 2016 does not erase three decades of hard feeling toward her and her husband from the right.”

But at least in recent weeks, it has been Clinton — who is actively promoting her new book, which she wrote with her daughter — who is driving much of the conversation. In a range of television interviews, she has expressed her support for House Democrats’ impeachment inquiry into Trump.

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The inquiry, she told ABC’s “The View,” was “absolutely unavoidable,” and it would have been “a dereliction of duty at that point for the Congress” not to have moved forward with an investigation of the president’s actions involving a controversial July 25 phone call he had with the president of Ukraine.

She has also been punchy, especially on Twitter. After Rudolph W. Giuliani, Trump’s personal attorney, chastised the media on Tuesday for not investigating “the Clintons and crooked Clinton Foundation,” Clinton offered a wry rejoinder: “Yes, I am famously under-scrutinized.” And after Sen. Kamala D. Harris (D-Calif.) offered a Twitter defense of Clinton following news of the State Department’s intensifying email probe of her former aides, Clinton replied, “But my emails. (Thank you.).”

“I hope @HillaryClinton never, ever goes away & always uses platform she has to advance causes of women & children, AND share her views on politics,” tweeted Jennifer Palmieri, Clinton’s 2016 communications director, adding “#MoreHillary.” Her tweet was in response to some anti-Clinton backlash from those who say Clinton should try to fade from public life.

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Trump also seems eager to keep Clinton around as a foil. On Thursday, during a speech at The Villages retirement community in Florida, a man shouted out “Lock her up!” and the president invited him to stand up.

“I admonish you,” Trump said sarcastically.

Shortly thereafter, the Clinton heckler shouted again, and the president returned to him.