Rick Scott, Florida’s Republican Governor-elect, was an early critic of President Barack Obama’s health-care overhaul, founding a group last year to fight what he called a bid for “socialized medicine.”

Scott will get another chance next month to derail the law Obama signed in March when he and 21 other Republican governors-elect are sworn in just as states begin implementing details of the legislation the candidates campaigned against.

Under the law, states have the authority to manage online insurance “exchanges” where as many as 24 million people can shop for coverage. It also gives them new funding to police premium increases. With Republicans winning 29 gubernatorial seats last month, up from 23 this year, insurers such as Hartford, Connecticut-based Aetna Inc. may face fewer restrictions and pay out less in benefits, said Michael Leavitt, a former health secretary under President George W. Bush.

“A lot of decisions are supposed to be made at the state level, and we think that works very, very well,” said Joseph Zubretsky, Aetna’s chief financial officer. “We have great relationships with state insurance departments.”

With voters concerned about rising health costs, the election may not give insurers a reprieve, said Sandy Praeger, a Republican re-elected as Kansas’ state insurance commissioner.

“It’s politically not very popular to have rates continue to go up and have a legislature or insurance commissioner not doing anything about it,” she said.

Republicans won governor races on Nov. 2 in Texas, Florida, Ohio and Pennsylvania, four of the seven most populous states, while losing in California and New York. They increased control of state legislatures to 25 from 14 this year, according to the Denver-based National Conference of State Legislatures.

Indianapolis-based WellPoint Inc., the top insurer by enrollment, expects to have losses of $150 million in California this year after politicians pressured it to scale back a rate increase.

The company is “cautiously optimistic that when we work with our regulators we can educate them on why losing money is not a sustainable business proposition,” said Wayne DeVeydt, chief financial officer after the company’s Nov. 3 earnings report.

WellPoint shares have fallen 12 percent since Obama signed the overhaul into law on March 30, while Aetna has lost 14 percent.

UnitedHealth Group Inc. of Minnetonka, Minn., the No. 2 insurer by sales, has gained 14 percent after raising its earnings forecast and announcing a higher dividend.

The health-care law requires insurers to spend at least 80 percent of policy premiums on patient care, instead of profits or administrative costs. Governors next year can request a waiver from the federal government if they conclude the mandate will destabilize insurance markets, said Leavitt, now a consultant to states and hospitals.

Governors and legislatures will then decide whether to participate in the exchanges, set to open in 2014, or to let the federal government run them, Leavitt said.  As many as 24 million people may shop for coverage in the online markets by 2019, the Congressional Budget Office estimated in March.

States that opt in will have to decide how much to regulate coverage inside the markets, said Leavitt, a former Republican governor in Utah. They could try to negotiate rates, mandate more benefits than the health-care law requires or ban sales outside the exchange, closing off a source of health-plan revenues, he said.

Republicans are also more likely to contract with private insurers, led by UnitedHealth Group Inc., to run state Medicaid programs for the poor while adding fewer restrictions on what they have to cover, Leavitt said. The health-care law expands Medicaid funding by $434 billion over the next decade.

States also will have to decide whether to apply for $250 million in grants the overhaul provides for insurer rate reviews, Praeger said. In some cases, states would have to revise their laws to do the reviews, she said.

The election results may mute criticism of insurer rate increases, after a year in which Obama and the Democrats blasted the industry for rising premiums, Praeger said.

Republicans targeted Obama’s overhaul during the campaign. John Kasich, Ohio’s incoming governor, said in a March 22 post on his campaign blog that the law would be a job-killer. Pennsylvania Attorney General Tom Corbett, elected as his state’s new chief executive, had already joined a lawsuit challenging the bill as unconstitutional.

Phone messages weren’t returned by Kirsten Page, a Corbett spokeswoman, or Rob Nichols, a Kasich spokesman.

In Florida, Scott isn’t eager to enforce any of the law and supports the lawsuit, said his spokesman, Trey Stapleton.

“The health-care bill was so poorly constructed, it is very unlikely Florida will take risks with our own tax dollars to operate something doomed to fail,” Stapleton said.

Scott founded the company that would grow into Nashville, Tenn.-based HCA Inc., the largest U.S. hospital chain, and told voters the experience will help him fix the health system. His past became a target for opponents, who cited the record $1.7 billion in federal fines HCA paid for allegedly fraudulent Medicare billing. Scott wasn’t charged with any wrongdoing.

In March 2009, he founded Conservatives for Patients Rights and vowed in a statement to support “free-market health care reform” and fight “Washington bureaucrats making decisions instead of doctors and patients.”

Republican electoral gains were “a pretty encouraging sign” for the industry, UnitedHealth CEO Stephen Hemsley told investors at a conference Tuesday.

The new governors will “move forward in a more real, practical way that will work within the realities of the individual states,” he said.