And, as she demonstrated here with a reminder to King’s old congregation that “there’s Jesus in every one of us,” she is opening up about herself to satisfy the electorate’s hunger for personal connection. Maybe even more striking than invoking Scripture, the scourge of Wall Street is spending some time with bankers: She attended a party fund-raiser in July at the summer residence of a former UBS executive, and also this summer she met privately in Washington with JPMorgan Chase’s chief executive, Jamie Dimon.
Mr. Sanders, however, appears to believe that no such nods toward pragmatism or convention are necessary in today’s Democratic Party. He is still surrounded by the same coterie of advisers, is remaining a political independent and is as convinced as ever that people will respond to his well-honed pleas to confront the billionaire class, provide health care for all and offer tuition-free access to college.
To the frustration of some of his advisers, Mr. Sanders has shown no willingness to veer from his social justice catechism to tell voters the personal details of his life’s journey, banking that an electorate that could elect Donald J. Trump to the White House no longer needs such political rituals.
Which of them is better able to broaden their appeal beyond the liberal white activists who crowd their public appearances could ultimately determine their prospects.
Perhaps most illuminating is the difference in how the two address a pair of intertwined issues: health care and President Barack Obama.
Defending the Affordable Care Act, Mr. Obama’s signature domestic legacy, is a staple of Ms. Warren’s speeches, and she takes care to salute the former president. “That’s a leader,” she said to applause in Atlanta, praising Mr. Obama for pushing through the health law.
While supportive of Mr. Sanders’s proposal for universal health care, her embrace of a single-payer system is aspirational and not nearly as central as protecting what she sees as the recent gains made to health care coverage. She is also looking for other incremental ways to expand coverage or lower the cost of care.
For Mr. Sanders, it is just the opposite: He was outspoken against Republican attempts to repeal the health law, but he is far less animated by defensive fights than by leading the movement toward a single-payer system.
As for Mr. Obama, Mr. Sanders sees the man who many Democrats believe will go down as one of the country’s greatest presidents as largely incidental to his vision. Speaking for just under an hour to thousands of supporters at his People’s Summit in Chicago last summer, Mr. Sanders made only a passing mention of Mr. Obama on the same weekend that Illinois’s governor, a Republican, was reportedly ready to sign a bill making the former president’s birthday a commemorative holiday in the state.
Certainly, a Warren nomination would underline how ascendant liberalism has become in the party, but to put Mr. Sanders forward as their standard-bearer would suggest that Democrats want to make a far more profound break from conventional politics. The party would have edged toward his brand of democratic socialism.
“The Democratic Party is a vehicle for him, but, for better and worse, he doesn’t embrace it or claim it,” said David Axelrod, the longtime Democratic strategist and former chief political adviser to Mr. Obama. “Elizabeth is much more supportive of the party even as she works to push it left.”
It is possible, of course, that the nominee will be neither Ms. Warren nor Mr. Sanders, and there will be no showdown. The three best-known candidates in a potential presidential field (to include former Vice President Joseph R. Biden Jr.) may all run or not run at all. And a host of other Democrats may be lining up for 2020 who could prove formidable, such Senators Kamala Harris of California and Cory Booker of New Jersey, former Gov. Deval Patrick of Massachusetts and current Gov. Steve Bullock of Montana.
Some admirers believe that Mr. Sanders and Ms. Warren are close enough to have a conversation about their intentions before they make a decision.
“Whether they figure it out is a different story,” said Larry Cohen, a former head of the Communications Workers of America union and an adviser to Mr. Sanders. “But would they talk about it? Absolutely.”
Some liberals are already dreading a Sanders-versus-Warren race in which they could take votes from each other. “I think it would be hurtful for the left,” said Symone Sanders, who worked for Mr. Sanders in the 2016 primary.
The two adopted New Englanders trace their history back to when Ms. Warren, still a professor, addressed a Sanders town hall-style meeting in Vermont at Mr. Sanders’s invitation. But the relationship grew strained when she declined to endorse him during last year’s primary.
In public, they appear to have moved beyond any raw feelings. Ms. Warren has joined Mr. Sanders’s podcast, and she made sure to group herself with him when she addressed Netroots Nation, a progressive conference, last month.
Advisers to Ms. Warren, eager to tamp down any hint of tensions, made a point of noting that the senator and her husband, as well as Mr. Sanders and his wife, found themselves with delayed flights at Reagan National Airport in Washington this year and used the time to catch up at an American Airlines lounge.
And Mr. Sanders is sensitive to the topic of his relationship with Ms. Warren: When the journalist Franklin Foer tried to ask him about it this year, “he peremptorily dismissed me from his office,” Mr. Foer wrote in The Atlantic.
Some of Mr. Sanders’s advisers, proud of how successful they were last year and determined to get their due, are less restrained.
“People talk about Elizabeth Warren, and I love Elizabeth Warren, but she doesn’t have a 50-state organization, and she doesn’t have an email list in the millions,” said Mark Longabaugh, who worked on Mr. Sanders’s primary campaign.
Those in the party more sympathetic to Ms. Warren, however, believe that she has far more potential to expand her appeal.
“I think Senator Warren’s views are more pragmatic; I think she is very different in a conversation than when she’s on the stump,” said Robert Wolf, the former UBS executive who hosted Ms. Warren and other Senate Democrats for a fund-raiser on Martha’s Vineyard this summer.
And then there is the biggest difference between them.
“One advantage she does have is the ability to broaden her base out because she can speak to women’s economic issues and women’s health in a way Sanders can’t do as well,” said Anita Dunn, a veteran Democratic strategist, noting that Ms. Warren’s silencing by Senator Mitch McConnell, the majority leader, in February had propelled her toward feminist icon status.
“I bought hand-quilted ‘She Persisted’ pillows on my vacation,” Ms. Dunn said, explaining that a gift shop in upstate New York had them for sale.
Ms. Warren, clearly conscious of the symbolic power of her run-in with Mr. McConnell, has turned the phrase into her own slogan-in-waiting, and invariably finds a way to sprinkle it in her public remarks. It is the sort of personal political touch for which Mr. Sanders has shown no appetite.
“Bernie is a great American story, but have enough people heard it? Probably not,” conceded Jeff Weaver, who managed Mr. Sanders’s presidential bid.
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