On a Saturday afternoon, Mr. Miller, a Vietnam veteran, told Mr. Meier about his positive experience with government health care through the Department of Veterans Affairs, saying, “I’ve seen how it can work.”

A few houses down, a woman who owns a cleaning service and would give only her first name, Sharon, and her party affiliation, Republican, said that if the bill covered abortions, “I won’t go for that.”

She added that she would be happy to stop paying $170 a month for supplemental insurance to cover what Medicare does not, but she did not want to see people who do not work receive free care. From the garage, her husband hollered that he agreed. Conceding defeat, Mr. Meier and Ms. Moss moved along.

Both Sanders supporters, they took on the cause in part because Ms. Moss has Type 1 diabetes and has struggled on and off to stay insured, though now she has Medicaid under the Affordable Care Act’s expansion of the program. Ms. Moss, 30, went to see Ms. Finkenauer in her district office this year and asked if she supported a government system that eliminated insurance. Ms. Finkenauer, she said, stated her preference for a public option.

“That’s simply a compromise that leaves the insurance companies still in the game,” said Mr. Meier, who recently started working at John Deere building backhoes and will soon have employer-based coverage after being uninsured for his entire adult life.

The Jayapal and Sanders bills would both expand traditional Medicare to cover all Americans, and change the structure of the program to cover more services and eliminate most deductibles and co-payments. There would effectively be no private health insurance, because the new system would cover almost everything; Mr. Sanders has said private coverage could be sold for extras like cosmetic surgery.