Nancy Downing, 42, a receptionist from Concord, said she admired Ms. Warren and Mr. Sanders for wanting to achieve free government health care for all. But she said Mr. Biden and Senator Amy Klobuchar of Minnesota, who has also proposed a public option, are more appealing to her because they are more realistic about long-term spending.

“They’re great ideals,” Ms. Downing said of the Warren and Sanders’ “Medicare for all” plans, “but I’m just not sure we can pay for it.”

The public option plans offered by Mr. Biden and Mr. Buttigieg would require much less federal spending than Ms. Warren’s $20.5 trillion proposal to provide generous health benefits, at no cost, to all Americans. Mr. Biden has estimated his plan would cost $750 billion over 10 years; Mr. Buttigieg has said his version, which he likes to call “Medicare for all who want it,” would cost $1.5 trillion.

Mr. Biden and Mr. Buttigieg ’s plans would automatically enroll uninsured Americans in the new government health plan and allow anyone else to opt in if they wished. Both candidates would offer more generous premium subsidies than the Affordable Care Act provides and cap people’s premium costs at 8.5 percent of their income. People with premium subsidies would have deductibles of roughly $1,000 or less. Mr. Buttigieg’s plan would go a step further, retroactively enrolling anyone who had remained uninsured but ended up sick.

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Although most of the other Democrats who qualified for Wednesday’s debate support the idea of a public option, few have released detailed proposals. Some candidates, like Senator Cory Booker of New Jersey and Andrew Yang, an entrepreneur, say they hope a public option would lead to “Medicare for all;” others, like Ms. Klobuchar and Tom Steyer, a former hedge fund investor and a billionaire, consider it an end in itself.

The public option that Ms. Warren has proposed as a bridge to her “Medicare for all” plan would go further. It would be free for all children and for households with incomes at or below 200 percent of the federal poverty level, which is currently about $51,000 for a family of four. For people who earn more, premiums would be capped at 5 percent of income; there would be no deductibles and “modest” out-of-pocket costs. Ms. Warren has not said how much this public option plan would cost the government, but it would be considerably less than “Medicare for all;” during Wednesday’s debate she said it would cover 135 million people — about 40 percent of the population — for free.