WAVERLY, Iowa — Sen. Elizabeth Warren (D-Mass.) pitched her new, more flexible approach to government-run health care during a town hall here Saturday afternoon as her campaign tries to move beyond an issue that’s mired her for weeks.

Under her proposal, outlined Friday, all Americans would be eligible to participate in Medicare, but it would not be mandatory. Warren said she’d push a full-fledged Medicare-for-all bill through Congress later in her first term.

“I want to do it early, early, early,” Warren told a crowd of nearly 600 at Wartburg College in northeastern Iowa. “There are millions of people right now who are struggling to pay their medical bills. Let’s get them in the door.”

Her new pitch also seems designed to assuage voters worried that her earlier approach would force 150 million people off their private insurance. Her ability to sell this new plan — and refocus her campaign on her larger message of reform — will be a key test for her candidacy.

The toll on her campaign is particularly apparent here in Iowa, where a new poll by the Des Moines Register and CNN released Saturday night showed Warren in a three-way tie for second place with former vice president Joe Biden and Sen. Bernie Sanders (I-Vt.), while South Bend, Ind., Mayor Pete Buttigieg surged ahead of the pack. The poll shows Buttigieg with 25 percent support and Warren, Biden and Sanders all with about 15 percent support.

Before this most recent poll, an average of five statewide polls since October showed Warren at 20 percent support among likely Democratic caucus-goers, Biden at 18 percent, Buttigieg at 17 percent and Sanders at 16 percent, with other candidates averaging 4 percent or less.

Warren has struggled to outline a plan for health care, saying earlier this month that she supports Sanders’s Medicare-for-all plan but would pay for it differently.

On Friday, she announced she will push Congress to pass legislation that allows all Americans to opt into the existing Medicare program in her first 100 days in office and take executive actions even sooner to lower the price of prescription drugs.

She wouldn’t push for full-blown Medicare-for-all until the third year of her term.

That has prompted Sanders to adjust, adding a line to his stump speech that contrasts Warren’s approach to his.

“Today I tell you that on our first week in office, we are going to introduce Medicare-for-all ­single-payer legislation,” he said Saturday in East Los Angeles.

Polls consistently show that Iowa Democrats say health care is their top issue and also that many Democrats have conflicted views about Medicare-for-all.

A recent New York Times-Siena College poll found that over 7 in 10 likely caucusgoers support “a single-payer health care system, which would abolish private insurance and provide every American with a government health insurance.”

But the same poll also found that more Democrats prefer a candidate who “promises to improve the existing health insurance system” rather than “replace the current health care system with Medicare-for-all.”

Several who attended Warren’s town hall Saturday were relieved by her new approach.

“I like the shift,” said Elizabeth Texley, 43, of Cedar Rapids. Texley works with seniors and hasn’t yet decided who she will support in the upcoming caucuses.

“The goal of Medicare-for-all is great,” she said. “But I don’t think you’re going to be able to get everybody on board right now.”

Warren’s new proposal, Texley added, “does make it easier to support her.”

Kristina Burroughes, 28, said she wants Medicare-for-all to happen quickly but believes Warren’s adjustment is smart strategy. “It’s walking into it instead of diving,” Burroughes said as she waited in line for a photo with the candidate.

In Iowa, Warren also tried to explain how her new plan differs from the proposal laid out by Buttigieg. Her plan, she argued, would get more people on government insurance for less money.

“Mine is about actually giving people Medicare-for-all that is going to be full health-care coverage,” she said when asked about the differences. “I’m going to bring in as many people as we can right at the beginning.”

Sean Savett, a spokesman for Buttigieg, said that the Buttigieg plan preserves private insurance for those who want it.Pete’s plan would also achieve universal health care coverage,” he said. “But unlike Senator Warren, he wouldn’t kick tens of millions of American families off their private health care plans because he trusts the American people to choose what’s right for them.”

But some voters didn’t detect a large difference between the two — aside from timing.

“She’s a week late for me,” said Conni Miller, 59 of Waverly, who came to Warren’s town hall even though she just committed to support Buttigieg largely because of his heath-care plan.

A key part of Warren’s gambit is to remain close enough to Sanders’s plan so that his voters would, at some point, support her. But among Sanders’s supporters gathered Saturday afternoon, there was deep skepticism.

“I think it’s terrible,” said Eduardo Barrio, 23, of San Bernardino, Calif. “She’s not going to be fighting for it.”

“There’s a gap [between] them,” he added. “She’s clearly the second-best option, but why have the copy when you can have the OG?”

Chelsea Janes in California and Scott Clement in Washington contributed to this report.