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President-elect Trump just promised that private insurance companies can help lower costs and get health insurance to more Americans.

But private health insurance already forms the basis of the Obamacare exchanges that Republicans have vowed to raze. And a conversation with just about any American covered by private health insurance makes it's immediately clear that the private health insurance industry is a source of many, if not most, of the frustrations of managing health insurance.

President-elect Trump just promised that private insurance companies can help lower costs and get health insurance to more Americans. But private health insurance already forms the basis of the Obamacare exchanges that Republicans have vowed to raze Joe Raedle / Getty Images

“We're going to get private insurance companies to take care of a lot of the people that can afford it. That's going to take a tremendous burden off and they're going to be able to have plans that are great plans,” Trump said in an interview aired Wednesday on the Fox news channel.

That’s pretty close to the goals of the 2010 Patient Protection and Affordable Care Act, widely known as Obamacare or the ACA.

“The ACA is a fairly free-market oriented health care proposal, more than I think many people on the left would have liked,” said Sherry Glied, dean of New York University’s Robert F. Wagner Graduate School of Public Service. “For the most part, companies can decide more or less what they want to do.”

Obamacare set up health insurance exchanges where people who couldn’t get good coverage any other way could go to buy policies regulated by the new rules, often with a generous federal subsidy.

It sought to stop the worst insurance company abuses, such as cutting off coverage when people got too sick, and sought to get rid of some of the most bare-bones plans that had low premiums but that also often left people in the lurch when they actually needed coverage.

Related: Five Things You May Not Know About Obamacare

Yet people still have struggled with denied claims, red tape and surprise medical bills, even on the Obamacare policies.

Abigail Leigh has been fighting with her provider, Anthem Blue Cross and Blue Shield in Virginia, to pay for an emergency visit she made last August to an urgent care clinic while visiting her home state of South Carolina.

“It became very painful to breathe,” Leigh, a pharmacy student in Richlands, Virginia, told NBC News.

“I had to take very short breaths to even breathe at all. I was starting to get a little dizzy. So we decided to go to urgent care."

“Now I’m having to call the hospital facility and keep them from sending the bill to collection."

The symptoms pointed to a potentially deadly blood clot in the lung, called a pulmonary embolism, so doctors ordered a battery of tests.

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Luckily for her it wasn’t. “He decided I must have pleuritis, which is an inflammation of the lining of my lungs,” said Leigh. The total bill: more than $1,700.

“I later on got a statement from my insurance company saying they won’t cover it.”

Leigh’s been going back and forth with the insurance company. Her $184-a-month policy, which she bought through the exchange that the federal government runs on Virginia’s behalf, doesn’t cover out-of-state care, unless it’s emergency care. Leigh argues that her case is clearly emergency care, but as of this week her appeal is still unanswered.

“Now I’m having to call the hospital facility and keep them from sending the bill to collection,” Leigh said. "I don't feel like I should be having to keep up on this."

Related: Obamacare Repeal Would Leave 18 Million Uninsured

It’s a problem that easily could have existed pre-ACA, but Leigh said these kinds of negotiations should have been addressed by the law.

The American College of Emergency Physicians (ACEP) lays the blame at the feet of the health insurance companies.

"No one chooses when they will need emergency care and should not be punished financially for having emergencies or discouraged from seeking medical attention when they are sick or injured,” said ACEP president Dr. Rebecca Parker.

"There have been significant reductions in insurance payments for emergency care, as much as 70 percent. They have taken gross advantage of patients and emergency medical providers since the ACA, arbitrarily slashing payments to physicians,” Parker added.

“They left me high and dry."

In some states, such as California, the exchanges have attracted many insurance companies and offer a variety of policies. In others, problems caused some insurance companies to abandon the exchanges, saying they can’t make enough money.

That’s what happened to Beverly Deeds, who lost her Blue Cross Blue Shield plan in Santa Fe, New Mexico when the insurer dropped off her state’s exchange. “They left me high and dry,” said Deeds, a 62-year-old retiree.

Related: Is the Obamacare Name to Blame for its Enemies?

The only insurer left for Deeds was Christus. Deeds had been paying $250 a month, with a $6,000 deductible, she said.

After making several phone calls, Deeds got a bronze-level Christus plan for $449 a month. The bare-bones bronze plans are meant to provide catastrophic coverage for people who are generally healthy.

“The deductible is just under $7,000,” she said. Her husband, who has Medicare coverage, earns too much for her to qualify for a federal subsidy or for Medicaid, even though New Mexico did opt in to the federal expansion of the program.

“I’m scared to death. If I got diagnosed with something, how would I pay with that $7000 deductible?”

“I hate it,” said Deeds, who says she voted against Obama but she says there’s plenty of blame to go around for what she sees as the ACA’s failures. “The insurance companies slanted things so they made a lot of money. Obamacare really padded their pockets,” she said.

Now, even though she qualifies for free annual mammograms and well-woman checkups, Deeds doesn’t go. “I’m scared to death. If I got diagnosed with something, how would I pay with that $7,000 deductible?” she asked.

“I think there’s a lot of frustration out there where this law was passed and was supposed to fix problems with the health care system, and people feel they are still paying a lot and don’t understand why the law hasn’t done more to help them,” said Liz Hamel, who leads polling for the nonpartisan Kaiser Family Foundation.

A report out this week from consultancy firm Avalere Health shows that the 11.5 million people getting health insurance on the exchanges in 2017 will pay more and often get less for their money than in previous years, although federal subsidies will close the gap for 81 percent of customers.

“Following several years of single-digit premium growth, premiums increased 12 percent on average for silver plans in 2017—from $496 per month in 2016 to $554 per month in 2017,” Avalere says.

Fewer than a third of policies are the preferred provider organizations (PPO) or point of service (POS) plans that offer customers a wide choice of doctors, hospitals and other providers. Deductibles for the silver plans – the plans that qualify for federal subsidies – grew by 20 percent for 2017.

America's Health Insurance Plans, which represents insurance companies, says prices depend on competition in each state, and says some of the ACA's rules have driven up costs. "Health insurance premiums are set based on a complex set of factors that reflect the cost of providing coverage in a state and in a market," it says.