Ms. Korchonnoff, 31, said the lawmakers should make health care available to all, especially low- and moderate-income people who do not qualify for existing government programs but struggle to afford insurance through the subsidized marketplaces created by the Affordable Care Act.

“Making it available to people who cannot afford to buy marketplace insurance is very important,” she said.

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The Times survey showed similar results when it came to “free college” proposals. About a third of Democrats said that the government should make public colleges free to low- and moderate-income families, but that the wealthy should still have to pay — again a policy close to that proposed by Mr. Buttigieg. Another third said that college should be more affordable but that most families should have to pay something. The remaining third expressed the most liberal position, that college should be free for all.

Voters also sounded a note of caution about the cost of candidates’ plans: Half of Democrats said the United States should adopt progressive proposals only if they do not increase the budget deficit, compared to 38 percent who said they supported the plans regardless of their fiscal impact. Both Mr. Sanders and Ms. Warren say they will pay for their plans through higher taxes, not through borrowing more money.

In interviews, voters gave different reasons for their positions. Some said they thought the most liberal positions went too far or questioned whether they would work in practice. Others were more focused on political strategy, concerned that liberal positions would hurt Democrats in the general election next fall.