Cindy Vinson and Tom Waschura are big believers in the Affordable Care Act. They vote independent and are proud to say they helped elect and re-elect President Barack Obama.

Yet, like many other Bay Area residents who pay for their own medical insurance, they were floored last week when they opened their bills: Their policies were being replaced with pricier plans that conform to all the requirements of the new health care law.

Vinson, of San Jose, will pay $1,800 more a year for an individual policy, while Waschura, of Portola Valley, will cough up almost $10,000 more for insurance for his family of four.

“Welcome to the club,” said Robert Laszewksi, a prominent health care consultant and president of Health Policy and Strategy Associates in Virginia.

For years, the nation has been embroiled in the political rhetoric of “Obamacare,” but this past week the reality of the new law sank in as millions of Americans had their first good look at how the 3﻿ 1/2-year-old legislation will affect their pocketbooks.

This much quickly became clear:

As state- and federal-run health insurance exchanges debuted across the country offering a range of prices for different tiers of insurance coverage, the new online marketplaces — which represent the centerpiece of Obamacare — could greatly benefit more than 40 million Americans who now lack coverage. But an additional 16 million — who buy individual health insurance policies on the open market — are finding out that their plans may not comply with the new law, which requires 10 essential benefits such as maternity care, mental health care and prescription drug coverage.

In California, 1.9 million people buy plans on the open market, according to officials with Covered California, the state’s new health insurance exchange. And many of them are steaming mad.

“There’s going to be a number of people surprised” by their bills, said Jonathan Wu, a co-founder of ValuePenguin, a consumer finance website. “The upper-middle class are the people who are essentially being asked to foot the bill, and that’s true across the country.”

Covered California spokesman Dana Howard maintained that in public presentations the exchange has always made clear that there will be winners and losers under Obamacare.

“Some people will see an increase who are already on the individual market purchasing insurance,” he said, “but most people will not.”

Covered California officials note that at least 570,000 of the 1.9 million people who buy their own insurance should be eligible for subsidies that will reduce their premiums.

Even those who don’t qualify for the tax subsidies could see their rates drop because Obamacare doesn’t allow insurers to charge people more if they have pre-existing conditions such as diabetes and cancer, he said.

People like Marilynn Gray-Raine.

The 64-year-old Danville artist, who survived breast cancer, has purchased health insurance for herself for decades. She watched her Anthem Blue Cross monthly premiums rise from $317 in 2005 to $1,298 in 2013. But she found out last week from the Covered California site that her payments will drop to about $795 a month.

But people with no pre-existing conditions like Vinson, a 60-year-old retired teacher, and Waschura, a 52-year-old self-employed engineer, are making up the difference.

“I was laughing at Boehner — until the mail came today,” Waschura said, referring to House Speaker John Boehner, who is leading the Republican charge to defund Obamacare.

“I really don’t like the Republican tactics, but at least now I can understand why they are so pissed about this. When you take $10,000 out of my family’s pocket each year, that’s otherwise disposable income or retirement savings that will not be going into our local economy.”

Both Vinson and Waschura have adjusted gross incomes greater than four times the federal poverty level — the cutoff for a tax credit. And while both said they anticipated their rates would go up, they didn’t realize they would rise so much.

“Of course, I want people to have health care,” Vinson said. “I just didn’t realize I would be the one who was going to pay for it personally.”

A frustrated Vinson went on the Covered California site to see what she would pay for the same policy if she lived in Los Angeles or Sacramento. She discovered she would save at least $100 monthly.

According to data compiled by ValuePenguin, Santa Clara County, San Mateo County, San Francisco as well as Santa Cruz, Monterey and San Benito counties have some of the highest health insurance rates in the state. Covered California officials say that in addition to the higher cost of living here, more hospitals in the Bay Area are owned by hospital groups that can demand higher rates because of the lack of competition.

Not all of the sticker shock can be blamed on Obamacare.

Health care inflation costs routinely increase at least 4 percent annually, said Ken Wood, a senior adviser for Covered California. Those increases, he noted, are due to an aging population and the rising costs of new medical technology and drugs, among other factors.

But Wood, Wu and others also said premiums will rise as a result of people getting better insurance under the new law, which requires most Americans, with few exceptions, to buy health insurance no later than March 31, or pay a minimum $95 annual penalty.

The law’s intent is to cover people who are now uninsured by making insurance accessible to everybody. But that means rates will rise for many because sick and healthy people will now be charged the same premium.

Adding a required list of 10 essential benefits to all plans is also significant. A study published last year in the journal Health Affairs said more than half of Americans who had individual insurance in 2010 were enrolled in plans that would not qualify because they didn’t meet all the new requirements.

Wood likened these mandates to the higher cost of buying cars today that must have safety features like air bags and anti-lock brakes.

The law also will often make some policies more expensive because it limits out-of-pocket expenses to $6,350 annually for an individual and $12,700 for a family. In addition, the law restricts the minimum and maximum premiums that people can be charged based on their age.

Now, a 64-year-old can be charged almost five times more than a 21-year-old. Beginning Jan. 1, it will be a 3-1 ratio.

Those explanations, however, don’t completely satisfy Waschura and Vinson.

“I’m not against Obamacare,” Waschura said. “It’s just the initial shock. I’m holding out hope that there will be a correction over a handful of years.”

But to Gray-Raine, the breast cancer survivor from the East Bay, that correction has already come.

“Obamacare is a huge step in the right direction for those of us without employer coverage,” she said, adding that she hopes everyone will “join in and make this new legislation a success for all.”

Contact Tracy Seipel at 408-275-0140. Follow her at Twitter.com/taseipel.