New York City resident Nicolas Karlson was happy to be one of at least 2.5 million people who beat a major Obamacare enrollment deadline last week, but he's going to be paying a lot more for health insurance next year because of it. To cover himself, his wife, Monica, and their three children, 45-year-old Karlson will go from paying $1,805 every three months for their long-standing Aetna plan, to a new one from New York State's Obamacare exchange that will cost them $1,221.60 per month, or more than 100 percent more than his old plan cost. That steep bump in price is a result of Aetna's reacting to a feature in the Affordable Care Act, a law that Karlson said of with a laugh, "I literally had no idea that it would affect me at all." That feature, as well as others in the ACA, motivated millions of people since Nov. 15 to sign up for health plans sold on government-run Obamacare marketplaces such as HealthCare.gov. The deadline for choosing plans that take effect Jan. 1 was Dec. 15 for federally run HealthCare.gov, which serves two-thirds of the U.S., but a number of state-run exchanges extended their own deadlines. Read MoreAbbVie gets exclusive hepatitis Cbilling

Tuesday is the deadline for Massachusetts, Washington state and Rhode Island. Exchanges in three other states (Vermont, Minnesota and Hawaii) have given residents until Dec. 31 to select plans that take effect the next day. The deadline for the New York State of Health exchange originally was Dec. 15, but officials extended it until last Saturday because of heavy snowstorms that affected the western part of the state last month.

People speak with an agent from Sunshine Life and Health Advisors, as they discuss plans available from the Affordable Care Act on Dec. 15, 2014, in Miami. Getty Images

Karlson, who runs a commercial production company, was unaware that New York had extended its deadline by five days, so he was scrambling two weeks ago to get new insurance. For six years or so, Karlson and his wife had an Aetna plan from a former employer of hers. Monica Karlson had kept the coverage via COBRA, which allows individuals to maintain their originally employer-provided coverage by paying for it directly. At some point the plan converted from COBRA, but the costs remained low. Several months ago, Aetna sent the Karlsons a letter "saying that our current plan is being canceled, and to go to the website and review plans that are available," Nicolas Karlson said. Despite that, the alternative were not posted for more than a month. And when Karlson looked at them, he was surprised. To get comparable coverage, he was looking at plans that cost between around $20,300 and $23,612 annually. He then called an Aetna rep. "I said, 'Right now, I'm paying $8,000 per year; what am I missing?' " Karlson recounted. "He said, 'That plan is discontinued.' He also said, 'I don't think that's what you're paying.' " "He said, '$1,800 per month,' and I said, 'No, $1,800 per quarter.' He said, 'Wow, you're really lucky,' " Karlson said. Read MoreMedicaid: Sign-ups at nearly 10M

But Karlson's luck had come to an end. The Affordable Care Act mandated a set of "essential health benefits" that all insurance plans had to cover, which included preventative services, ER visits, pediatric vision and dental care and mental health care. That mandate rendered many plans non-compliant with the law. Pre-existing plans, or grandfathered plans, were allowed to continue under the ACA, but only if insurers made no significant changes to coverage. And in response to the troubled launch of HealthCare.gov last year, the Obama administration has allowed the option of other non-compliant plans continuing through 2017.