Feeling lighter in the wallet and unhappier about Obamacare? You're not alone. Support for the Affordable Care Act has plummeted since late last summer, and people with employer-based health insurance say they increasingly are paying more for out-of-pocket medical expenses, a new Bankrate.com survey released Wednesday revealed. When Bankrate.com first polled people in September—right before the launch of Obamacare insurance exchanges, there was an even split between those who said they would repeal the Affordable Care Act if given the power to do so and those who would keep it: 46 percent each. (The rest either had no opinion or didn't know how they felt.)

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But three months later, after the botched launch of those government-run exchanges, the number of people who said they would gut Obamacare had risen to 48 percent, while the number of respondents who said they would keep it as law had plunged to 38 percent.

(Read more: Obamacare first-person series: Real people, real stories) The survey also found that people, by a 2-to-1 margin, felt Obamacare had had a more negative than positive impact on their own, individual health care. The poll questioned 1,005 adults, and had a margin of error of 3.6 percentage points. "We have seen a softening in support of the law," said Doug Whiteman, Bankrate.com insurance analyst. "I really think that stems from all the adverse publicity in the last several months" that focused on the technologically crippled federal Obamacare exchange and the resulting low enrollment in the first two months of operation, he said.

His company's survey also found that a total of 44 percent of people with employer-provided insurance said they are shelling out more dollars in deductibles and copayments than they were a year ago. And 47 percent of that group of people reported having more money deducted from their paycheck to pay the cost of those insurance plans than in 2012. People earning between $50,000 and $75,000 annually were the most affected group: with 64 percent of them reporting a bigger hit on their paychecks from health insurance. Just 38 percent of the people earning less than $30,000 reported paying more for insurance in payroll deductions as of 2013. 'Cadillac tax' wallop Whiteman attributed the jump in the number of people reporting increases in their out-of-pocket expenses to companies anticipating Obamacare's so-called Cadillac tax, which beginning in 2018 will levy a 40 percent tax on company insurance benefits that exceed $10,200 for an individual and $27,500 for a family. "Some employers are citing the Cadillac tax as the reason they are paring back some of their health insurance benefits," Whiteman said. Increasing deductibles—which forces employees to pay a bigger share of their medical care and possibly may make them more price-conscious about using their benefits—is one strategy companies are using to address the tax. He said that trend will "most definitely" strengthen the closer it gets to 2018. But insurance executive David Sterling, while saying anticipation of that tax has played some role in employees paying more for their health costs, contended that a number of other Obamacare mandates are spurring the upward trend of insurance prices. (Read more: Health spending shrank for first time as share of GDP in 2012: Officials)

"One of my clients called me yesterday, he has a small group, with a few employees, and United [HealthCare] sent out a communication that the premium went up 18 percent, and [it] had already gone up about 20 percent in 2013," said Sterling, CEO of Sterling Healthworks, the health-care reform arm of SterlingRisk. "I'm getting calls from my customers, they're saying, 'Who can afford these premiums, we've never seen premiums this high.' "

Sterling cited the Obamacare mandate that requires health plans to cover the adult children of their customers up to age 26, and the requirement that plans include certain minimum essential benefits as a reason for the premium increases. He also said that the employer mandate, which as of 2015 will require companies with more than 50 full-time workers to offer health insurance, also is playing a role in driving up prices. "I would say that for at least the last ... year and a half, we have been making radical changes to employers' plans in reaction to other employer mandates," said Sterling. (Read more: Flu blues for business: Influenza may hit more working-age folks)

While inflation in deductibles and copayments was occurring even before the adoption of the Affordable Care Act in 2010, Sterling said that trend "has accelerated because employers are preparing for their greatly increased costs" from providing insurance to workers. But health policy expert Judy Feder, a Georgetown University professor, said it was "ridiculous" to blame increases in out-of-pocket costs on Obamacare. "It seems to me that it was something that is increasing anyway," said Feder, who is also a fellow with the Urban Institute think tank. "I think the impact on the costs from the ACA is minimal."