“She wants to have open borders,” he added, voicing another reason that some people in Rockland think a President Warren won’t protect them. (Like a number of the Democratic presidential candidates, Ms. Warren is in favor of decriminalizing unauthorized border crossings.) And the sense that Ms. Warren, who has voted in Congress for a ban on assault weapons, is soft on gun rights also plays into the notion that she would leave Rockland unprotected. The 49-year-old voted for Mr. Trump in 2016 and fully plans to do so again in 2020, with the “good job” the president is doing on the economy. (After speaking to me, he climbed into a car with a National Rifle Association sticker affixed to the back windshield.)

As Ms. Warren’s Senate campaigns attest, she is by no means uniformly unpopular in Rockland or, for that matter, in neighboring communities with a similar socio-economic profile.

“I love Elizabeth Warren,” said a welder and member of a plumbers union local, age 68, by phone. “She’s my bulldog. She is 100 percent for us — for the working man, the exploited person, the underdog.” He is from Weymouth, next door to Rockland. “If she were a man, they would love her.” He paused. “Or they would like her more.”

As he explained, places like Rockland, on the South Shore of Massachusetts, need to be understood as products of “white flight” from Boston, following court-ordered school busing in the mid-1970s.

Should she win the Democratic nomination, it’s easy to see the difficulties she will face in gaining the allegiance of the white working class in a matchup with Mr. Trump. White flight also defines a number of working-class suburbs in the Midwest, as in the metropolitan Detroit region.

But even though the Warren Paradox will be a real challenge, she still has the opportunity to impress potentially unreceptive voters with her “bulldog” tenacity, as in her visit this year to a small town in West Virginia to talk about the opioid crisis — a state, 93 percent white, taken by Mr. Trump in 2016 by nearly 42 points. She has also put gut economic issues at the centerpiece of her agenda: For instance, her “Plan for Economic Patriotism,” an industrial-policy tack calling for such steps as “more actively managing” the currency value of the dollar “to promote exports and domestic manufacturing” and a tenfold increase in government spending on job apprenticeship programs, won praise from the Fox News commentator Tucker Carlson. “It’s just pure old-fashioned economics: how to preserve good-paying American jobs,” he told his audience, a form of “economic nationalism.”

And to be sure, while white working-class voters get a great deal of attention in battleground states like Michigan, if Democrats can increase turnout among African-American voters in 2020, that would help counterbalance any weakness among white working-class voters.