The stick's getting a lot bigger — but it's not clear that many more people will choose the carrot as a result. Households that opt to go without health insurance in 2016 are set to get hit with an average Obamacare fine of $969.

That is 47 percent higher than the average $661 penalty per uninsured household for this year, a new analysis by the Kaiser Family Foundation revealed Wednesday. And households without insurance that earn too much to qualify for financial aid to buy Obamacare plans will pay an even larger fine for 2016 — an average of $1,450, versus the average of $1,177 for 2015. Uninsured households that would qualify for Obamacare subsidies to help pay for coverage face an average fine of $738 — nearly double the $389 average for this year. "It's a substantial increase," said Larry Levitt, senior vice president at the Kaiser Family Foundation, about the higher average fines.

The Kaiser analysis also found that 3.5 million uninsured people could buy coverage with a $0 monthly premium, or plans that would still cost less annually than what their fine would be for not having insurance, Kaiser's report said.

But 7.1 million people who are currently uninsured would pay more money if they bought the least-expensive health insurance plans available during the current open enrollment season than they would if they just paid the penalty, Kaiser said.

The report underscores what Kaiser called "a key area of uncertainty": The extent to which higher Obamacare penalties will prod uninsured people to sign up for coverage. More sign-ups in turn could strengthen the financial situation of health plans being sold on government-run exchanges. Open enrollment in Obamacare plans is going on now, and will end Jan. 31.

In an effort to boost sign-ups this season, Obama administration officials have been highlighting the financial aid for which most customers of government-run health exchanges qualify. The aid is designed to help them pay their monthly premiums. "After financial assistance, 7 out of 10 people can find plans with premiums of less than $75 per month," Kevin Counihan, CEO of the federal Obamacare exchange HealthCare.gov, wrote in a blog post Tuesday.

I do think that over the next couple of years, the increasing penalties will have a noticeable effect on enrollment. Larry Levitt senior vice president, Kaiser Family Foundation

Counihan and other officials have been pointing out that Obamacare penalties for going without insurance are rising this year. But it's not clear, as yet, whether that message is being heard by the uninsured. "It's not top of the mind for most people," Levitt said. "The penalty is only effective if people know about it," said Levitt. "If people go on HealthCare.gov now, they can find out how much the insurance costs them. But it's less obvious what the penalty is for remaining uncovered." The penalty for not having health coverage in 2015 is the higher of $325 per adult, or 2 percent of adjusted household income. People who didn't have coverage this year, and who did not qualify for an exemption from the fine, will pay the penalty when they file their income tax returns in early 2016. The penalty is set to rise in 2016 to the higher of $695 per adult, or 2.5 percent of household income. But, again, the penalty will come due only during the 2016 tax filing season, which begins in early 2017.