A small but noticeable polling bump suggests that Elizabeth Warren is beginning to gain traction with Democratic voters, staking a strong claim to third place behind front-runner Joe Biden and Bernie Sanders. Warren stumbled early out of the gate with a mis-timed rollout and an ill-conceived debate over her Native American ancestry, but has since differentiated herself from the rest of the Democratic field with a raft of detailed (and budget-busting) policy proposals to solve everything from the crippling student debt to the nation’s deadly opioid crisis. Perhaps more striking, it appears she’s making inroads among some Trump voters, too.

Politico trailed the Massachusetts senator to Kermit, West Virginia—a town in the reddest of states, decimated by OxyContin—where voters were reportedly receptive to her $100 billion plan to tackle the opioid crisis, and came away with newfound appreciation for her gumption, if not her politics. “She’s a good ol’ country girl like anyone else,” said LeeAnn Blankenship, who voted for Trump in 2016. “She’s earned where she is; it wasn’t given to her. I respect that.”

Folksiness alone doesn’t win elections, and even with her stacks of policy papers, Warren is still polling fairly low among Democrats. But a demonstrated ability to converse with Trump voters, to address the cultural and economic problems plaguing the post-industrial hinterlands of Appalachia and Wisconsin and Western Pennsylvania, will be key to retaking the White House. Voters who swung from Barack Obama to Trump in 2016 haven’t forgotten the condescending way that Hillary Clinton talked about the “deplorables” and coal-mining jobs that aren’t coming back. (Others remember how Obama spoke contemptuously of people who “cling to guns or religion.”) The 2020 Democratic field has, on the whole, taken these sorts of grievances more seriously than in the past. Biden, for one, is building his entire campaign on the theory that he can uniquely connect with the middle class; Pete Buttigieg has painted himself as the pothole-filling mayor of a small post-industrial city; and Cory Booker is exuding a blinding message of cross-partisan love. But Warren, like Sanders, has established a laser focus on bread-and-butter issues that speak to the “forgotten” men and women who bet big on Trump, but are beginning to wonder if they backed the wrong horse. No other candidate has proposed as many policies to actually improve those people’s lives.

Trump Country is surprisingly receptive to Warren’s vision. In a recent focus group observed by Axios in Sioux city, Iowa, voters who flipped from Obama to Trump “strongly supported” Warren’s plan to cancel up to $50,000 in student debt for voters whose families made less than $100,00 a year. They echoed her message that many Americans are not reaping the benefits of a booming economy, pointing to stagnant wages and a declining quality of life. And there was a strong consensus that big financial institutions should be taxed to pay for infrastructure.

The only catch? The focus group wasn’t told that the student debt plan was Warren’s. All but 1 of the 11 Obama-Trump swing voters in the group said they would re-elect Trump if he were running against Clinton. They weren’t excited about any of the Democrats who were running, including Warren. And one of them stated that “the presidency is a man’s job.”

Trump, of course, has no intention of waging the campaign over which candidate’s policies actually benefit his base. But these anecdotes do seem to confirm that the market for liberal ideas is broader than is commonly supposed, and the right kind of Democratic campaign could exploit it. Trump, after all, ran on preserving Social Security, Medicare, and Medicaid; withdrawing from international free-trade deals; instituting five-year lobbying bans on White House officials and members of Congress; and cracking down on tax loopholes favored by hedge funds and private equity, among other policies that might appeal to the W.T.O. protest set.