The Obama administration has pointed to the drop in uninsured people as proof that Obamacare is working, but a new survey shows that while more people are getting coverage, many workers who get insurance from their employers are paying a lot more out of pocket for healthcare.

That's because this year, more people are on high-deductible health plans, which require workers to pay a greater share of expenses, according to a survey released Tuesday from the Kaiser Family Foundation. Even those that aren't on high-deductible plans are paying higher deductibles, the survey found.

The foundation looked at employer-sponsored health plans, which are still the most common way Americans get health insurance.

It found that while premiums are relatively stable, workers are paying more in annual deductibles. A deductible requires the insured worker to pay a certain amount before the insurance kicks in.

Younger and healthier workers usually take high-deductible plans because they are cheaper than regular plans, and many don't expect to use it as much. But more companies are pushing those plans because they can lower healthcare costs, since workers on such plans spend a larger share on their healthcare needs.

That could impact the health care people actually receive. A study released earlier this year showed that a worker on a high-deductible healthcare plan is more likely to skip procedures and less-pressing healthcare services because of the higher costs. But the study emphasized that its findings need to be examined further as the results were limited to only those in a large company.

Obamacare was designed to help lower healthcare costs, and 2014 data shows that healthcare spending grew at the slowest rate since 1960. The law also created new rules for cost-sharing for insurers as a way to keep premiums down.

The average deductible for single coverage is $1,318 a year, close to last year's figure of $1,217, Kaiser said.

However, that deductible has increased about $400 from 2010.

About 24 percent of all covered workers are enrolled in a high-deductible plan, compared to just 13 percent in 2010.

The amount of a deductible differs by company size. Workers in small companies pay an average of $1,836 for a single-coverage deductible, compared to $1,105 for workers in larger companies, Kaiser's report said.

A majority of workers in smaller companies (60 percent) tend to have a plan with a deductible of at least $1,000 for single coverage, compared to 39 percent for large firms, according to the survey of nearly 2,000 companies.

The same goes for deductibles that are even higher. Kaiser found that 36 percent of workers in small firms had a deductible of at least $2,000, while just 12 percent of people faced that level at larger companies.

The problem is that all deductibles appear to be going up, not just for those people in high-deductible plans. Kaiser said that the share of covered workers in plans with a general annual deductible has increased significantly, from 55 percent in 2006 to 81 percent this year.

"If we look at the change in deductible amounts for all covered workers (assigning a zero value to workers in plans with no deductible), we can look at the impact of both trends together," the report said. "Using this approach, the average deductible for all covered workers in 2015 is $1,077, up 67 percent from $646 in 2010 and 255 percent from $303 in 2006."

The survey also touched on other ways workers are paying more for healthcare. For instance, about 98 percent of all workers are in plans with an out-of-pocket maximum for single coverage, more than the 88 percent in 2013, the survey found.

About 13 percent of plans had an annual maximum of $6,000 or more and 9 percent less than $1,500.

Americans also are paying more for prescription drugs, an issue that has gotten a lot of attention from the Democratic primary field. Hillary Clinton on Tuesday officially announced a plan to combat high prices, while Vermont Independent Sen. Bernie Sanders issued legislation earlier this month with a similar set of reforms.

Kaiser officials said that high-cost deductibles, alongside high drug prices, are shaping up to get a lot of attention in the next election.

"With deductibles growing much faster than wages … deductibles and drug costs could emerge as the next big health issue, not instead of the Affordable Care Act but alongside the Affordable Care Act," said Drew Altman, president and CEO of the Kaiser Family Foundation, in a Tuesday call with reporters.