Two years ago, Alexandria Ocasio-Cortez, then a young, untested democratic socialist, pulled off a shocking upset by defeating the No. 4 House Democrat, Representative Joseph Crowley. The primary result was a visceral warning to Democratic leadership that it had better quickly reckon with the push for progressive change, and not underestimate the candidates behind it.

The Democratic establishment has apparently heeded that lesson.

As the June 23 primary nears in New York, another long-tenured Democrat, Eliot L. Engel, is being threatened by a young progressive challenger, Jamaal Bowman. The race has become a focal point for the party’s directional battle, with money and marquee endorsements flying around in recent days.

The latest big-name endorsements came in a span of 16 hours: On Monday afternoon, Hillary Clinton, making her first endorsement of any Democratic incumbent facing a primary in 2020, backed Mr. Engel; the following morning, Senator Elizabeth Warren of Massachusetts endorsed Mr. Bowman.

Mr. Engel, 73, seems to be the party’s most vulnerable incumbent in the nation at the moment, a potential victim of its emboldened left wing, which has grown impatient with the establishment politics that Mr. Engel seems to represent.

Mr. Engel, the chairman of the House Foreign Affairs Committee, is a Democratic stalwart, a faithful practitioner of old-school Washington politics, rising in committee ranks and bringing home perks for his diverse and overwhelmingly Democratic district at New York City’s northern border.

Mustachioed and bespectacled, Mr. Engel’s most famous trait may be his punctuality: He prides himself on arriving early to each and every State of the Union, to secure a seat to shake the president’s hand — a tradition that he has halted in opposition to President Trump. But in a political landscape upended by the coronavirus and the national reckoning on race and policing, Mr. Engel’s press-the-flesh approach is at risk of seeming like an anachronism.

Mr. Bowman, 44, has the support of Senator Bernie Sanders of Vermont and Ms. Ocasio-Cortez, the generational tent poles of progressive Democrats, as well as liberal groups like the Working Families Party and political action committees like the Justice Democrats, which jointly pledged to spend more than $500,000 to oust Mr. Engel.

Senator Warren, the former presidential candidate and possible vice-presidential contender, said on Tuesday that Mr. Bowman was “exactly the kind of person we need in Congress fighting for big, structural change.”

Mr. Engel has widespread support from senior House Democrats, including Speaker Nancy Pelosi; James E. Clyburn, the House majority whip; and Hakeem Jeffries, the House Democratic Caucus chairman.

But Mr. Engel has not exactly helped his cause. In early June, at a news conference in the Bronx devoted to Black Lives Matter, he was caught on microphone suggesting that he was only there because of his contested race. “If I didn’t have a primary,” he said, “I wouldn’t care.”

Even party veterans cringed. “This is like hanging a sign from your neck saying, ‘I’ve been in office too long,’ ” tweeted David Axelrod, the Democratic strategist.

Asked about the comment, Mr. Engel did not address it directly but said that he had “wanted people to know how I feel because I feel so strongly about what happened” in the aftermath of the killing of George Floyd by the police in Minneapolis.

“In looking back, I see now that two weeks later that my words have detracted from the protests because they’ve been taken out of context,” he said. “And I want to use my voice to refocus on the fact black lives matter. And they do.”

Both Mr. Engel and Mr. Bowman have embraced many of the positions championed by Ms. Ocasio-Cortez, who represents a neighboring district in the Bronx and Queens, including the Green New Deal and Medicare for all.

Mr. Engel’s campaign website also cites support for increased funding public education, $100 billion in new housing, and comprehensive immigration reform. But his opponents have zeroed in on several hawkish positions he took, including rejecting the Iran nuclear deal in 2015 and supporting the invasion of Iraq more than a decade before.

“You know, I’m pretty progressive myself,” Mr. Engel said in an interview last week from his home in the Bronx. “I have a progressive record down the line for many years in Congress and I’m proud of my record.”

Despite the recent successes of some progressive insurgents, it is still extraordinarily difficult to unseat a congressional incumbent in a primary; this year, only two have fallen, each under unusual circumstances.

In Illinois, Representative Dan Lipinski, a conservative Democrat who had broken with his party on abortion rights and health care, lost to Marie Newman in a rematch in March; in Iowa, Representative Steve King, a Republican with a history of racist remarks, lost to Randy Feenstra, a state senator.

Mr. Bowman is hoping that a different sort of circumstances may catapult him to victory.

The coronavirus outbreak and civil unrest after Mr. Floyd’s killing complicated the campaign for both candidates, forcing the cancellation of in-person events and fund-raisers. But they also gave Mr. Bowman, who is African-American, a conducive environment to stress the need for change in arenas like criminal justice and health care.

Mr. Bowman was recruited by Justice Democrats after education activists in New York suggested he could be a potent candidate with a compelling life story: a childhood in public housing in New York City, followed by years as an educator, culminating with the founding of a middle school in the Bronx, the Cornerstone Academy for Social Action, where he was the founding principal.

Mr. Bowman began this campaign last June, with several other challengers, including a lawyer, Chris Fink; Sammy Ravelo, a retired police lieutenant; and Andom Ghebreghiorgis, who dropped out earlier this month and endorsed Mr. Bowman, solidifying his support among progressives.

“We’ve anchored our race in fighting for racial and economic justice from the very beginning,” Mr. Bowman said in an interview. “And what Covid and now these protests are revealing is, to the rest of the country, is how broken our system is.”

The dueling crises also provided Mr. Bowman with a powerful talking point accusing Mr. Engel of not spending enough time in the district, which includes the northern Bronx and portions of southern Westchester County, a mix of well-to-do neighborhoods like Riverdale and poorer areas.

Mr. Bowman has repeatedly attacked Mr. Engel’s staying at a home he owns in Maryland during long stretches of the coronavirus virus outbreak, as well as for much of his time in Washington.

“He doesn’t live in our community,” Mr. Bowman said in one online testimonial. “I live in our struggles.”

This argument seems to befuddle Mr. Engel, who said he bought the Maryland home after he was first elected in 1988 and had two small children at the time.

“I work in Washington and he’s going to deny me a place to sleep?” Mr. Engel said, adding, “You can’t stay on the, sleep on the, streets.”

As the race has intensified, Mr. Engel has also fought back, pointing out that election records show that Mr. Bowman did not vote in 2012, even as Barack Obama — still the lodestar of many Democratic voters — sought a second term. Mr. Bowman insists that he remembers voting in Manhattan that year, saying “there must be a problem with the records.”

“Do you think I wouldn’t vote for the first black president?” he said.

Mr. Engel also highlighted how Mr. Bowman only registered as a Democrat in 2018; he was previously registered in the Independence Party. “So he’s not really a Democrat,” Mr. Engel said.

Voters in the district have been inundated with mailers and phone calls on behalf of both candidates, who have already spent a combined $2 million on the race, and will likely spend more in the closing days. As of June 3, Mr. Engel still had more than $800,000 in hand, compared with Mr. Bowman’s $345,000.

In Hastings-on-Hudson in Westchester, Jim Cullen, 57, a self-described moderate Democrat, said he would vote for the incumbent, though he knew his wife and son would vote for Mr. Bowman, saying it was good to “preserve the institutional integrity of the Democratic Party at a time when it’s under tremendous pressure.”

But Olivia Lovejoy, 40, said she was ready to embrace Mr. Bowman’s message.

“I’m thinking we need change,” said Ms. Lovejoy, a customer service representative, adding that Mr. Bowman’s candidacy gave her cause for optimism. “I feel hopeful.”

For his part, Mr. Engel seemed well aware of the tentative nature of his political perch.

“I never forget for even one moment that this is the people’s seat,” he said. “And not my seat.”

Nate Schweber contributed reporting.