A plan by House Republicans, which was released last week, would repeal major parts of Mr. Obama’s health care law and would phase out the expansion of Medicaid that has brought coverage to millions of people.
Senate Democrats cast a wary eye on how Ms. Verma might enforce the legislation, if it is approved. Mr. Wyden said she “would be able to give states a green light to push the very frail and sick into high-risk pools” in which they could receive substandard coverage or be forced to pay more for the care they need. Senator Maria Cantwell, Democrat of Washington, said Ms. Verma in Indiana “made millions of dollars in consulting fees by kicking poor, working people off of Medicaid for failure to pay monthly contributions similar to premiums.”
And Senator Debbie Stabenow, Democrat of Michigan, said she was dismayed that Ms. Verma had suggested at her confirmation hearing last month that coverage of maternity care should be optional, not required, as it is now under the Affordable Care Act.
At that hearing, Ms. Verma said: “Some women might want maternity coverage and some women might not want it, might not choose it, might not feel like they need that. So I think it’s up to women to make the decision that works best for them and their families.”
But not all Democrats found fault with Ms. Verma’s work on Medicaid in Indiana. Under the program she helped devise, “hundreds of thousands of Hoosiers currently have health insurance,” said Senator Joe Donnelly of Indiana, one of three Democrats who voted for her on Monday.
“This plan,” he said, “has helped lower our state’s uninsured rate and improve health care outcomes, and has played a critical role in combating the opioid-abuse and heroin-use epidemics.”
The Obama administration granted a waiver for Indiana’s Medicaid program following lengthy negotiations, and several other states are considering similar changes. Tom Price, the secretary of health and human services, promised last week to give states “greater flexibility.”
Judith Solomon, a vice president at the Center on Budget and Policy Priorities, a liberal-leaning research and advocacy group, said the premiums charged to Medicaid beneficiaries in Indiana, as well as the complexity of the program, appeared to be “deterring significant numbers of eligible low-income people from enrolling.” Still, she said, the coverage provided under Indiana’s plan is “better than no coverage at all.”
And without the conservative features of the program, state officials said, Indiana might not have expanded eligibility.
Dennis M. Murphy, the chief executive of Indiana University Health, and top executives of five other hospital systems in Indiana endorsed Ms. Verma, saying in a joint statement that she had shown a knack for “bipartisan solutions that unite people across the political spectrum.”
The Centers for Medicare and Medicaid Services has led federal efforts to carry out the Affordable Care Act, setting standards for private health insurance and operating HealthCare.gov, the online marketplace on which more than 10 million people obtained coverage last year.
Ms. Verma has comparatively little experience with Medicare, the popular program that insures 57 million people who are 65 or older or have disabilities. Within a decade, enrollment is expected to grow by one-third, to 76 million. As a presidential candidate, Mr. Trump said he did not intend to cut Medicare or Medicaid.