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NEW YORK—The tens of thousands of people who crowded into Washington Square Park and waited through a light rain to hear Elizabeth Warren speak yesterday evening already knew her as the 2020 candidate with the plans.

That much was clear when the first big roar of the night went up about a third of the way into the senator from Massachusetts’s 40-minute speech. “I know what’s broken. I’ve got a plan to fix it, and that’s why I’m running for president of the United States,” she declared, lifting and opening up her arms as if to receive the crescendo of cheers. “There it is.”

This simple summation of her candidacy, and its even shorter distillation—“Warren has a plan for that”—are the closest she gets to a “Yes we can”–like bumper-sticker slogan. She has many plans, in fact: pages upon pages of proposals to supersize the federal government and reshape the American economy. Among them are calls for a Green New Deal, universal child care, a major expansion of Social Security, the cancellation of most student-loan debt, and a 2 percent wealth tax on households with a net worth of more than $50 million. Warren came to New York to sell her latest offering: a plan to curtail lobbying that she billed as “the most sweeping set of anti-corruption reforms since Watergate.”

Yet if Warren’s candidacy is premised not only on progressive ambition but on the sheer breadth and specificity of her agenda, her growing support with Democrats may not be. Her fans like that she has plans, but it’s not the details they seem to be attracted to. Nor is their support based on a belief that Warren can deliver the scale of transformation she’s promising; indeed, nearly all of the attendees I spoke with yesterday expressed a deep skepticism that her agenda is truly achievable.

“I don’t necessarily think everything she puts out will get done. The Senate is the Senate,” Kolbi Brown, a 33-year-old hospital program manager, told me, referring to the GOP’s majority in the chamber. “I understand that it’s a system and she’s only a part of it.”

Brown said he was leaning toward voting for Warren but remained “very pessimistic” that Congress would enact such a far-reaching agenda. “I think she speaks the truth,” Brown said of Warren. “It’ll be a big boulder to push up the hill.”

Brown was attending the speech with his colleague, Rhonda Trousdale, a 53-year-old physician who told me that she and her friends call Warren “the kindergarten teacher” because of her ability to explain and boil down complex topics during the financial crisis. “She understands that things are really complicated,” Trousdale said.

I asked whether Trousdale believed that Warren could accomplish many of her goals if elected president. She paused. “They’re ambitious,” she replied. “Probably when she gets in office she’ll find that a lot of that is unrealistic.”

A pair of public-school teachers, Elizabeth Sweeney and Christine Ellrodt, both 59, hadn’t firmly committed to Warren, but they said they were attracted to her in part because of her detailed policy plans. “She seems to have really thought about everything,” Ellrodt told me. “I love the fact that she has a plan for everything. I really do.”

When the question turned to how realistic Warren’s ideas were, however, both women were unsure. Sweeney noted the uncertainty about the makeup of Congress. “All these executive orders isn’t the way to go either,” she told me, referring to the habit of recent presidents trying to go around recalcitrant lawmakers by acting unilaterally. “At least she has some ideas and we’re not starting from scratch,” Sweeney said of Warren.

The gap between the scale of Warren’s agenda and the difficulty in enacting it could be a challenge for her as the primary rolls on, as it is for her main competitor on the left, Senator Bernie Sanders of Vermont. The current front-runner, former Vice President Joe Biden, is pitching himself as a dealmaker, not a disruptor, who can forge consensus in Congress and build on the achievements of Barack Obama’s administration. Warren’s also battling doubts about her ability to beat Donald Trump, as Democrats worry about whether her agenda is too far left for the country, whether Republicans will succeed in attacking her past attempts to claim Native American ancestry, and whether sexism in the electorate will keep yet another woman from the Oval Office.

In New York, Warren devoted a large portion of her speech to convincing the crowd that “big, structural change” was possible. She told the story of the Triangle Shirtwaist Factory fire, which occurred just one block east of the park where Warren spoke, and of Frances Perkins, who seized on the 1911 tragedy that killed 146 garment workers to galvanize support for a raft of new worker-protection laws. Perkins would later become the first woman to serve as a Cabinet secretary, under President Franklin D. Roosevelt. Warren described how Perkins “pushed on the inside” while women’s trade unions applied pressure on the outside of government to help enact FDR’s New Deal.

“The time for holding back is over,” she said, mocking those who have dismissed her agenda as “too big, too hard.”

“We can’t choose a candidate we don’t believe in just because we’re too scared to do anything else,” Warren continued, in what appeared to be a dig at Biden. “I am not afraid, and you cannot be afraid either.”

If Warren’s many policy plans are detailed and specific, her strategy for achieving them is less so. Summoning the legacy of Perkins, she suggested that a grassroots movement of outside pressure would help make her agenda a reality. Yet that was also Obama’s plea, and while the former president was able to enact the Affordable Care Act, Wall Street reforms, and a large economic-stimulus package early in his tenure, his entreaties for outside help did not succeed in pressuring Republicans to support his plans.

“The Republican gang has to be beat,” Sandy Fletcher, 69, told me before Warren spoke.

And why, I asked, would she succeed when Obama did not?

“At least her skin is the right color,” Fletcher replied. “It was because he was black that they gave him so much trouble.”

Fletcher told me that she’s wanted Warren for president for the past four years. “I just don’t know how far she’ll get if she’s elected, if [Mitch] McConnell is in the Senate,” she said.

But that worry did not dim her support for Warren. “I believe her,” Fletcher said, “and I believe in her.”

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