“The leaders of the majority party in the House and Senate are likely to reflect the views of their party’s adherents,” two Harvard University scholars concluded in The New England Journal of Medicine. Their view is supported by public polling that shows a highly partisan assessment of the law. A Harvard School of Public Health poll in September found that 83 percent of Republican likely voters say they want the law repealed or scaled back, an overwhelming sentiment that would be hard to ignore if Congress is in all-Republican hands next year.

But Mr. Obama would veto any attempt to repeal the law, so Republicans are left with lesser options.

Under Mr. Gillespie’s plan, tax credits would be used by those without access to employer-provided health care to buy insurance on the individual or small-group market. People with an existing medical condition could not be dropped or see premiums rise as long as they maintained constant coverage. Those with existing health problems who could not find health plans would go to “high-risk pools” run by the states but financed with $7.5 billion in federal funds, an amount that would rise 3 percent a year.

According to the Center for Health Economy, whose board includes conservative and liberal health care economists, the plan would leave about six million fewer people insured in a decade, primarily because it would roll back Medicaid expansion. But, the center said, it would also lower the cost of less comprehensive health insurance plans, expand access to health care providers and cost $1 trillion less than the Affordable Care Act.