He tried to extend health insurance to the entire population through a system of subsidies for the uninsured working people and extending eligibility for free insurance for the poor.
When Trump announced in November that he was appointing Verma for the post, he said that she would be a part of "the dream team that will transform our healthcare system for the benefit of all Americans".
Her role will extend beyond the insurance programmes - Medicare for senior citizens and Medicaid for the poor - to helping craft and implement the Republican healthcare reform plan to replace Obamacare.
"She has decades of experience advising on Medicare and Medicaid policy and helping states navigate our complicated systems," Trump had said.
Verma, who is close to Vice President Mike Pence, helped develop a public healthcare system for implementing Obamacare in Indiana where he was the Governor.
Among other things, her system there required those using it to make contributions to it, even if it was a nominal dollar by the poorest, to ensure they felt responsible and involved. It was opposed by many Democrats.
California Democrat Senator Diane Feinstein, who voted against her appointment, said that making the poorest to pay for insurance was one of the reasons she opposed Verma.
Obamacare was enacted in 2010 against stiff opposition by most Republicans and Trump promised during his campaign to repeal it.
Ironically, many of his supporters who opposed Obamacare may now find themselves without health insurance.
The Republican plan to replace Obamacare could lead to 14 million people losing health insurance, according to the research office of the Congress sparking fierce opposition to it.
It also faces stiff opposition from the right wing of the Republican Party, which opposes subsidies and sees any government-mandated health programme as state intrusion in peoples' lives.
Under Obamacare those who did not get health insurance or dropped it had to pay fine.
Manny Sethi, an Indian-American doctor who runs a non-profit health organisation in Tennessee, was among a group that met Trump on Monday to complain about Obamacare.
"So what they are doing is, effectively, they're paying the tax penalty because it's cheaper and works out better than paying for the insurance."
Medicare that Verma will oversee provides insurance for over 46 million senior citizens, who are a politically powerful block, and Medicaid has about 60 million poor people enrolled in it.
Together they are about a third of the US population.
There are nearly 60,000 doctors of Indian descent working in the US, making them an important constituency for healthcare reforms.
Verma's appointment was welcomed by Ajay Lodha, the president of the Association of American Physicians of Indian Origin.
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