The proposal’s chance of success is dubious. Colorado has a mixed record when it comes to ballot measures, though it has passed some notable ones over the years, including marijuana legalization and the Taxpayer Bill of Rights, an anti-tax, anti-spending constitutional amendment.

But the proposal had enough support to garner 100,000 signatures, which put it on the ballot. It has also worried insurers, and some in the medical community and the business community, enough for them to organize in opposition, even enlisting a Democratic former governor to help in their campaign.

In this season of political discontent, the notion of dismantling the health insurance system has tapped an aquifer of frustration from voters. People say that even after the Affordable Care Act, they still pay too much in premiums, plus thousands in deductibles, and still have to worry about being bankrupted by a disabling car crash or an extended hospital stay.

“I think insurance is one of the biggest jokes and crooks,” said Brandon Barta, 38, of Denver. He said his father, Dixon, who worked at a gas station, never received aggressive enough treatment for his prostate cancer. He died last May at the age of 64.

“He was overlooked,” Mr. Barta said.

Mr. Barta said he was intrigued by the idea of a universal health plan that covered maternity care, checkups, emergency room visits and hospital stays, all the way through end-of-life care. Like millions of Americans, he has health insurance tied to his work. His coverage lapsed recently when he switched jobs to start working for a golf entertainment complex, and he is still waiting for his new plan to kick in.