In contrast to the dire pronouncements from President Trump and other Republicans, the demise of the individual insurance market seems greatly exaggerated, according to a new financial analysis released Friday.

The analysis, by Standard & Poor’s, looked at the performance of many Blue Cross plans in nearly three dozen states since President Barack Obama’s health care law took effect three years ago. It shows the insurers significantly reduced their losses last year, are likely to break even this year and that most could profit — albeit some in the single-digits — in 2018. The insurers cover more than five million people in the individual market.

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After years in which many insurers lost money, then lost even more in 2015, “we are seeing the first signs in 2016 that this market could be manageable for most health insurers,” the Standard & Poor’s analysts said. The “market is not in a ‘death spiral,’ ” they said.

It is the latest evidence that the existing law has not crippled the market where individuals can buy health coverage, although several insurers have pulled out of some markets, including two in Iowa just this week. They and other industry specialists have cited the uncertainty surrounding the Congressional debate over the law, and the failed effort two weeks ago by House Republicans to bring a bill to the floor for a vote.

The House G.O.P. leadership went home for a two-week recess on Thursday, unable to reach a compromise between conservative and moderate members over the extent of coverage that should be required for the very sick.

If the markets were to falter without a resolution in Congress, the risk of eroding public opinion before the midterm elections next year is bound to increase. The latest monthly Kaiser Health Tracking Poll by the Kaiser Family Foundation showed that more than half of Americans now believe that the president and Republicans own the health care issue and may shoulder the blame for any failings. The survey reported that more than half now support the Obama health care law.

The S.&P. report also buttresses the analysis of the Republican bill by the Congressional Budget Office, which said the markets were relatively stable under the current law, contradicting some Republican assessments of volatility.

“Things are getting better,” Gary Claxton, a vice president at the Kaiser Family Foundation, said of the insurance markets. The foundation has been closely tracking the insurers’ progress.

Although it took longer than expected, the insurers appear to be starting to understand how the new individual market works, said Deep Banerjee, an S.&P. credit analyst who helped write the report. The companies have aggressively increased their prices, so they are now largely covering their medical costs, Mr. Banerjee said. They have also significantly narrowed their networks to include fewer doctors and hospitals as a way to lower those costs.

In 2016, the number of companies whose medical costs exceeded their premiums fell by half, to nine of the 32 Blue Cross companies included in the S.&P. analysis. The improvement signaled the potential for profit margins to increase. A few plans, notably Florida Blue, are already profitable. The report released on Friday did not include Anthem’s for-profit Blue Cross plans, which span 14 states.

Mr. Banerjee warned that the market is still fragile, and he said insurers needed more time to figure out how to make the business work. While the market is very much alive, he said, it is “still in critical care. It still needs time to improve.”

The S.&P. report represents some good news in a market that has proved more than challenging to the health insurers. Most insurers have struggled to make money, and several companies reported losses that ran into the hundreds of millions of dollars.

News media have reported on insurers that are giving up. Aetna and UnitedHealth Group were among the first major insurers to largely pull out, but, early this year, Humana announced it would stop selling policies in 2018. That could leave parts of Tennessee without any insurers, an outcome that some senators on both sides of the aisle are trying to address.

Just this week, two of the three largest insurance companies in Iowa, Wellmark Blue Cross and Aetna, said they would stop selling individual policies in the state next year. That could leave nearly all of Iowa with only one carrier.

The insurers’ latest withdrawals are helping to fuel Republicans’ arguments that they have no choice but to repeal the law. Mr. Trump has continued to proclaim that he believes the market will collapse without a new law.

It is unclear what he and Congress will do to fundamentally change the insurers’ projections for next year. While Mr. Banerjee predicted insurers would probably raise their prices only moderately next year, he said questions over whether there would be as much government financing could lead to much sharper increases. The companies appear likely to make money in 2018, but “there are external events that could stop that,” he said.

Under the Republican proposal, called the American Health Care Act, several provisions could upend coverage for a variety of customers, Mr. Claxton said. The insurers could be selling to a new group of customers, if lower-income customers lose the subsidies they now receive and cannot afford higher prices.

Mr. Claxton warned that there could be markets that would have no insurance companies offering coverage, particularly in rural areas where there were not many to begin with. “How to fix that was always going to be an issue,” he said.

Caroline Pearson, a senior executive at Avalere Health, predicted that more insurers would decide there was no real future for the market, given the political environment. Even if they are close to making money, they may decide it is not worth the headache. Many of the companies are still losing money or are at risk of losing money if they sign up too many people who are sick.

“If you are an insurer and think the exchange is here to stay, your tolerance for annual losses is higher,” she said, “and it’s a long-term strategy.”