U.S. HIGHWAY 20, Iowa — Leaning back on a black leather sofa as her campaign bus rumbled toward Fort Dodge, Sen. Kamala Harris tried to explain why she spent months defending a plan to replace private health insurance with “Medicare for All,” only to switch to a more modest proposal that would allow private insurance to continue after all.

“I don’t think it was any secret that I was not entirely comfortable — that’s an understatement,” Harris said. “I finally was like, ‘I can’t make this circle fit into a square.’ I said: ‘We’re going to take hits. People are going to say she’s waffling. It’s going to be awful.’?” But, she said, she decided it was worth it.

The Democratic senator from California is hardly alone. The idea of Medicare for All — a unified government health program that would take over the basic function of private insurance — became a liberal litmus test at the outset of the presidential campaign, distinguishing Democratic contenders who cast themselves as bold visionaries from more moderate pragmatists.

But in recent months, amid polling that shows concern among voters about ending private insurance, several of the Democratic hopefuls have shifted their positions or their tone, moderating full-throated endorsement of Medicare for All and adopting ideas for allowing private insurance in some form.

“What I think has happened in the Democratic primary is people recognize that some of the concerns about single-payer are not coming from special interests but the public,” said Neera Tanden, a former top aide to Hillary Clinton and now president of the Center for American Progress. (A government-run health system is sometimes called a single-payer system.)

Harris’ new plan would allow private insurance policies as long as they followed Medicare’s rules on quality and price, giving consumers a choice much like the one seniors currently have between Medicare and Medicare Advantage plans.

Former Texas congressman Beto O’Rourke, who in 2017 embraced Medicare for All as the “best way,” now similarly supports a plan that would preserve the current employer-based insurance system.

This unmistakable, if sometimes subtle, shift in tone stems in part from Democrats’ fear of giving away a newfound advantage over Republicans on health care.

After the Affordable Care Act passed in 2010, Republicans scored major political victories by vowing to repeal the initially unpopular law. But when the GOP seized control of Washington under President Trump and tried to follow through on those promises, they faced a powerful backlash from voters who’d come to rely on the ACA.

Now some Democrats warn of the perils for their party in taking a position that, to important groups of voters, could seem just as disruptive as the GOP’s push to kill the ACA.

“There is nothing more personal to people than their health care,” said Kathleen Sebelius, who consulted on Harris’ plan and served as health and human services secretary in the Obama administration. “Anything that calls for the vast majority of Americans to lose what they have — that’s a very dangerous place to start a conversation.”

Five of the seven U.S. senators in the race have co-sponsored the Medicare for All bill drafted by Sen. Bernie Sanders, I-Vt. But they have begun to shade their messages, suggesting that the bill represents a long-term vision rather than an immediate plan.

Many of the candidates are now focusing on steps they say would push the country closer to universal health care without a major disruption, such as creating a “public option” that would let people join Medicare without making it mandatory.

Sen. Cory Booker of New Jersey, for example, co-sponsored the Sanders bill and emphasizes that he still supports it, but he describes himself as a “pragmatist” who would focus on “the immediate things we would do,” which do not include eliminating private health insurance.

Many Democrats argue that if Americans are given the choice of a public, government-run health option like Medicare, they will eventually see it as preferable to the private system and will migrate there on their own. That would create a government-run system without coercing people to join it, they say.

Sen. Kirstin Gillibrand of New York, another co-sponsor of Sanders’s bill, stresses this approach. “I can go to anywhere in this country and say, ‘Why not have a not-for-profit public option that competes with your insurer charging you too much money?’?” Gillibrand said Monday during a Washington Post Live event.

Even Sen. Elizabeth Warren of Massachusetts, who declared “I’m with Bernie on Medicare for All” at the first Democratic debate, has given herself wiggle room, saying that “there are a lot of different pathways” to achieving the goal of the Sanders bill.

Sanders himself is emphasizing his continued allegiance to a sweeping version of Medicare for All. That shows, he suggests, that he is the only candidate who can be trusted to fight for real change.

His campaign argues that allowing private insurance to remain, with all its inequities and privileges, would only perpetuate a tiered health care system.

“The moment a person has to open their wallet to get health care in America is the moment that some people will be denied that right,” said Ari Rabin-Havt, chief of staff for Sanders’s campaign. “Anyone supporting plans that would leave millions without even basic coverage cannot claim to be standing for health care as a right.”

Still, Sanders has begun facing pushback on the campaign trail. At two stops in Iowa on Monday, he was asked whether Medicare-for-all would hurt the health plans of unionized workers, which have been negotiated to provide significant benefits. Sanders argues that Medicare-for-all would result in better coverage at a lower price.

Similar concerns are reflected in surveys. A Washington Post-ABC News poll in July found that 52 percent of Americans overall, and 77 percent of Democrats, prefer a universal health program to the current system. But support dropped to 43 percent and 66 percent, respectively, when respondents were told that it would mean eliminating private insurance.

Other surveys have found less support. About 8 in 10 Democrats and Democratic-leaning independents in a Pew poll in July said the federal government has a responsibility to ensure health coverage, but less than half said it should be through a single government plan.