Secret conversations are taking place in Florida between healthcare stakeholders and the legislature that will most likely lead to the Republican-controlled state accepting Medicaid expansion money, according to senior figures in the health industry.

Some health professionals believe the amount of money on offer and the fact that the Republican party benefits from campaign contributions by the health insurance industry means that Florida is likely to find a way take the funding provided by the Affordable Care Act.

It would join a number of states with Republican-dominated legislatures, including Arkansas, Iowa and Wisconsin, to exploit a provision in the ACA that allows them to take the additional cash by providing an alternative to the public Medicaid program.

Donna Shalala, secretary for health and human services under Bill Clinton and now president of the University of Miami, told journalists at a meeting convened by the Kaiser Family Foundation in Miami this week that Republicans in the state would find a way to get over their political opposition to the ACA, also known as Obamacare.

“When people say to me, is Florida ever going to come around, my answer is yes, because a billion dollars is on the table and the stakeholders are big contributors to the Republicans – to the party. They understand that it will be a major economic investment in the state and they are just trying to figure out a way around the ideology in the conversations that are going on,” said Shalala, speaking to journalists at the publicly funded Jackson Memorial Hospital, which partners with the University of Miami.

Shalala's view was supported later by Patrick Geraghty, president and chief executive of the insurance company Florida Blue, who has been involved in discussions in the state and nationally. “We believe strongly that we ought to be taking that funding,” he said. The money should be used to support change and innovation in healthcare systems. “For our state it's $51bn over 10 years. That's a lot of investment in transformation.”

States can access the federal funds either if they expand the public Medicaid programme or, as permitted under the legislation, if they come up with an alternative way to fund expanded coverage. To qualify for Medicaid expansion money, however, an alternative system must be granted a waiver by federal authorities. Geraghty said she believed Florida would “do the right thing” and undertake an expansion.

“I don't believe it will be Medicaid – I think our state legislature will come up with some alternative and bring that forward,” he said. “But frankly I think getting started is the important thing and I hope that we put something out there that the federal government can make a decision on whether they give us a waiver or not.”

Only half of all states have agreed to expand Medicaid as President Obama wanted and the Affordable Care Act originally envisaged. The supreme court upheld the personal mandate, arguably the most controversial aspect of the healthcare reform bill, but ruled that states could not be required to expand Medicaid.

Many of those states that are turning their back on expansion, in spite of the federal government subsidy which is 100% for the first three years, are in the south and have the lowest rate of health insurance coverage in the US. They include Texas, Mississippi and Alabama, as well as Florida. Expanding Medicaid to 138% of the federal poverty level, which is everybody earning less than $15,800 a year, would have enrolled an additional 16 million people. In Florida, this would have given health insurance to a million more people.

The largest numbers set to benefit from Medicaid expansion are in California, where six million of the state’s population of 24 million are uninsured. California has agreed to expand its Medicaid system.

Most Republican states are turning their backs on expansion, but some are trying to make compromises with the electorate in mind. Wisconsin already runs a generous Medicaid programme, known as BadgerCare, brought in when the state was under Democratic leadership. Republican governor Scott Walker plans to cut Medicaid for 77,000 people with incomes above poverty line, but will lift a cap on the numbers who can enrol, which will allow in around 83,000 poor adults without children to join for the first time.

Michigan's Republican governor Rick Snyder signed Medicaid expansion into law in September with bipartisan support. "This is about the health of fellow Michiganders," said Snyder at the time. "The right answer is not to talk about politics, but to talk about our family of 10 million people."

The White House believes opposition to expansion in the red states will gradually crumble. The substantial financial incentives make economic sense, said Shalala. “It's hard to believe at the end of the day that economic incentives won't work – as powerful as these economic incentives,” she said. Healthcare formed a very large part of the economy of Florida, she said.

Governor Rick Scott has already said he would take the Medicaid expansion money for three years. “I think the senate has some people that are prepared to play and are prepared to shape some kind of a framework for taking the Medicaid money,” she said.

Shalala played down the significance of the healthcare.gov website meltdown and President Obama's decision to allow people with cancelled, sub-par insurance policies to keep them for another year. “It looks like you're running backwards, but sometimes you back up a little before you go forwards,” she said.

She pointed out that the number of people involved in the cancellation amnesty is a small percentage of the total that will benefit from the Affordable Care Act. Over the next year, most will discover that they can get better insurance at a reasonable price, and the whole system will begin to work better.

“This is a tiny part of the market – it's 5% of the market. And I believe that a large percentage of people in that market, once they calm down and get the information about what their alternatives are, are going to take advantage of those alternatives. But what it [the extension] did was kind of give them assurance that there's a floor under them and the floor is the assurance they've had before. So in the long run, I'm not convinced it's going to have a huge impact even if the insurers aren't too happy because their deal was everybody's in and that's the only way we can spread the risk.”

Beyond the current controversy over the performance of the federal website, and policy cancellations, a big question for the success of the Affordable Care Act is whether enough young and healthy people people sign up for insurance, to balance out older, less healthy people and those with pre-existing conditions.

Shalala said it was too early to tell: “With people coming in slowly and we're not too sure of the mix, I'm not sure we can come to conclusions that this is a disaster – except in Washington, where it's pure politics.”